InstaQB

Home
Institutions
- Institutions
  
  Polytechnic Colleges
  
  Medical Colleges
  
  Arts & Science Colleges
  
  Universities
  
  Engineering Colleges
  
  Agricultural Colleges
  
  Research Institute
  
  Law Colleges
  
  Audiology and Speech Colleges
  
  Business & Management colleges
  
  Nursing colleges
  
  Hotel Management institutes
  
  Aeronautical Colleges
  
  Bachelor's Degree
Syllabus
Courses
Stateboard
- 12th Standard English Medium
  
  Maths
  
  Physics
  
  Chemistry
  
  Biology
  
  Computer Science
  
  Business Maths
  
  Economics
  
  Commerce
  
  Accountancy
  
  History
  
  Computer Applications
  
  Computer Technology
  12th Standard Tamil Medium
  
  உயிரியல்
  
  கணினி பயன்பாடுகள்
  
  கணினி அறிவியல்
  
  வணிகக் கணிதம்
  
  வணிகவியல்
  
  பொருளியல்
  
  கணிதவியல்
  
  வேதியியல்
  
  இயற்பியல்
  
  கணினி தொழில்நுட்பம்
  
  வரலாறு
  
  கணக்குப்பதிவியல்
  11th Standard English Medium
  
  Maths
  
  Commerce
  
  Economics
  
  Biology
  
  Business Maths
  
  Accountancy
  
  Computer Science
  
  Physics
  
  Chemistry
  
  Computer Applications
  
  History
  
  Computer Technology
  
  Bio - Zoology
  11th Standard Tamil Medium
  
  கணிதவியல்
  
  உயிரியல்
  
  பொருளியல்
  
  இயற்பியல்
  
  வேதியியல்
  
  வணிகக் கணிதம்
  
  கணினி அறிவியல்
  
  கணக்குப்பதிவியல்
  
  வணிகவியல்
  
  கணினி பயன்பாடுகள்
  10th Standard English Medium
  
  Mathematics
  
  Science
  
  Social Science
  
  9th Standard English Medium
  
  Mathematics
  
  Science
  
  Social Science
  
  8th Standard English Medium
  
  Mathematics
  
  Science
  
  Social Science
  7th Standard English Medium
  
  Mathematics
  
  Science
  
  Social Science
ICSE/ISC
- Class XII
  
  Mathematics
  
  Physics
  
  Accountancy
  
  Biology
  
  History
  
  Geography
  
  Psychology
  
  chemistry
  
  Economics
  
  Computer Science
  
  Political Science
  
  Business Studies
  Class XI
  
  Accountancy
  
  Chemistry
  
  Mathematics
  
  Biology
  
  Geography
  
  Physics
  
  History
CBSE
- 12Th Standard
  
  Physics
  
  Chemistry
  
  Maths
  
  Biology
  
  History
  
  Economics
  
  Commerce
  
  Geography
  
  Socialogy
  
  Business Studies
  
  Computer Science
  
  Biotechnology Class
  
  Political Science
  
  Home Science
  11Th Standard
  
  Physics
  
  Chemistry
  
  Maths
  
  Biology
  
  History
  
  Economics
  
  Commerce
  
  Socialogy
  
  Business Studies
  
  Geography
  
  Home Science
  
  Computer Science
  
  Biotechnology Class
  
  Political Science
  10Th Standard
  
  Physics
  
  Chemistry
  
  Biology
  
  Mathematics
  
  Economics
  
  Geography
  
  History & Civics
  
  Computer Application
  9Th Standard
  
  Physics
  
  Chemistry
  
  Biology
  
  mathematics
  
  Computer Application
  
  Economics
  
  Geography
  
  History & Civics

11th Maths Weekly Test -1 (Vector Algebra)

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test -1 (Vector Algebra)-Aug 2020

Time : 1.30 Hours

Part - A

Multiple Choice Question - Answer All Question

If \(\left| \vec { a } \right| \)=4 and \(-3\le \lambda \le 2\) then the range of \(\left| \lambda \vec { a } \right| \)is

[0, 8]
[-12, 8]
[0, 12]
[8, 12]

Find the odd one out of the following

\(\hat { i } +2\hat { j } +3\hat { k } \)
\(2\hat { i } +4\hat { j } +6\hat { k } \)
\(7\hat { i } +14\hat { j } +21\hat { k } \)
\(\hat { i } +3\hat { j } +2\hat { k } \)

The vector having initial and terminal points as (2, 5, 0) and (-3, 7, 4) respectively is

\(-\hat{i}+12\hat{j}+4\vec{k}\)
\(-5\hat{i}+2\hat{j}-4\vec{k}\)
\(-5\hat{i}+2\hat{j}+4\vec{k}\)
\(\hat{i}+\hat{j}+\vec{k}\)

If (1, 2, 4) and (2, - 3\(\lambda\) - 3) are the initial and terminal points of the vector \(\hat{i}+\hat{j}-7\hat{k}\) ,then the value of \(\lambda\)is equal to

\(7\over 3\)
-\(7\over 3\)
-\(5\over 3\)
\(5\over 3\)

If \(\overrightarrow{a}\) and \(\overrightarrow{b}\) are two vectors of magnitude 2 and inclined at an angle 60° , then the angle between \(\overrightarrow{a}\) and \(\overrightarrow{a}+\overrightarrow{b}\) is

30°
60°
45°
90°

If m \(\left( \overset { \rightarrow }{ 2 } +\overset { \rightarrow }{ j } +\overset { \rightarrow }{ k } \right) \) is a unit vector then the value of m is

\(\pm \frac { 1 }{ \sqrt { 3 } } \)
\(\pm \frac { 1 }{ \sqrt { 5 } } \)
\(\pm \frac { 1 }{ \sqrt { 6 } } \)
\(\pm \frac { 1 }{ {2 } } \)

If \(\overrightarrow{a}=\hat{i}+\hat{j}+\hat{k},\overrightarrow{b}=2\hat{i}+x\hat{j}+\hat{k},\overrightarrow{c}=\hat{i}-\hat{j}+4\hat{k}\) and \(\overrightarrow{a}.(\overrightarrow{b}\times \overrightarrow{c})=70,\) then x is equal to

5
7
26
10

The projection of \(\overrightarrow { b } \) on \(\overrightarrow { a } \) is

\(\left( \frac { \overrightarrow { a } .\overrightarrow { b } }{ |\overrightarrow { b } | } \right) \overrightarrow { b } \)
\(\frac { \overrightarrow { a } .\overrightarrow { b } }{ |\overrightarrow { b } | } \)
\(\frac { \overrightarrow { a } .\overrightarrow { b } }{ |\overrightarrow { a } | } \)
\(\left( \frac { \overrightarrow { a } .\overrightarrow { b } }{ |\overrightarrow { a } | } \right) \)

Assertion (A) : \(\overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } ,\overset { \rightarrow }{ c } \) are the position vector three collinear points then 2 \(\overset { \rightarrow }{ a }=\overset { \rightarrow }{ b } +\overset { \rightarrow }{ c } \)
Reason (R): Collinear points, have same direction

Both A and R are true and R is the correct explanation of A
Both A and R are true and R is not a correct explantion of A
A is true but R is false
A is false but R is true

If \(\overrightarrow{a}=\hat{i}+2\hat{j}+2\hat{k},|\overrightarrow{b}|=5\) and the angle between \(\overrightarrow{a}\) and \(\overrightarrow{b}\) is \({\pi\over 6},\) then the area of the triangle formed by these two vectors as two sides, is

\(7\over4\)
\(15\over4\)
\(3\over4\)
\(17\over4\)

Part - B

Generic 2 - Answer All Question

Find the angle between the vectors \(2\vec { i } +\vec { j } -\vec { k } \) and \(\vec { i } +2\vec { j } +\vec { k } \) by using cross product.

Find the value \(\lambda\) for which the vectors \(\overrightarrow{a}\) and \(\overrightarrow{b}\) are perpendicular, where \(\overrightarrow{a}=2\hat{i}+\lambda\hat{j}+\hat{k}\) and \(\overrightarrow{b}=\hat{i}-2\hat{j}+3\hat{k}\)

If \(\vec{a}=\hat{i}+2\hat{j}+3\hat{k}\) , \(\vec{b}=-\hat{j}+4\hat{k}\)and \(\vec{c}=\hat{i}-2\hat{j}+\hat{k}\). Find\((\vec{a}+\vec{b}).\vec{c}\) and \(\vec{c}.(\vec{a}+\vec{b})\) Are they equal?

Find \(|\overrightarrow{a}\times \overrightarrow{b}|,\)where \(\overrightarrow{a}=3\hat{i}+4\hat{j}\)and\(\overrightarrow{b}=\hat{i}+\hat{j}+\hat{k}\).

Part - C

Generic 3 - Answer All Question

Find the projection of \(\overrightarrow{AB}\) on \(\overrightarrow{CD}\) where A, B, C, D are the points(4, - 3, 0), (7, - 5, - 1),(- 2, 1, 3), (0, 2, 5).
The vertices of a triangle have position vectors \(4\hat { i } +5\hat { j } +6\hat { k } ,5\hat { i } +6\hat { j } +4\hat { k } ,6\hat { i } +4\hat { j } +5\hat { k } \) Prove that the triangle is equilateral.

If (a,a+b,a+b+c) is one set of direction ratios of the line joining (1, 0, 0) and (0, 1, 0), then find a set of values of a, b, c.

Let A and B be two points with position vectors 2\(\overrightarrow{a}\)+ 4\(\overrightarrow{b}\) and 2\(\overrightarrow{a}\) −8\(\overrightarrow{b}\). Find the position vectors of the points which divide the line segment joining A and B in the ratio 1:3 internally and externally.

Shown that the points with position vectors \(\vec { a } -2\vec { b } +3\vec { c } -2\vec { a } +3\vec { b } +2\vec { c } \) and \(-8\vec { a } +13\vec { b } \) are collinear.

Part - D

Generic 5 - Answer All Question

If \(\overrightarrow{a},\overrightarrow{b}\)are unit vectors and \(\theta\) is the angle between them, show that \(cos {\theta \over 2}={1\over2}|\overrightarrow{a}+\overrightarrow{b}|\)

Find the projection of the vector \(\hat{i}+3\hat{j}+7\hat{k}\) on the vector\(2\hat{i}+6\hat{j}+3\hat{k}\).
If \(\overrightarrow{a},\overrightarrow{b}\)are unit vectors and \(\theta\) is the angle between them, show that \(tan {\theta \over 2}={|\overrightarrow{a}-\overrightarrow{b}|\over|\overrightarrow{a}+\overrightarrow{b}|}\)

A triangle is formed by joining the points (1, 0, 0), (0, 1, 0) and (0, 0, 1). Find the direction cosines of the medians.

If G is the centroid of a triangle ABC, prove that \(\overrightarrow{GA}\)+\(\overrightarrow{GB}\) +\(\overrightarrow{GC}\) = \(\overrightarrow{0}\).

Comment

Add Comment

Tamilnadu Stateboardszs - Class