11th Maths Monthly Test - 4 ( Vector Algebra )

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test - 4 ( Vector Algebra )-Aug 2020

Time : 2.00 Hours

Part - A

Generic 5 - Answer All Question

If D is the midpoint of the side BC of a triangle ABC, prove that \(\overrightarrow{AB}\) + \(\overrightarrow{AC}\) = 2\(\overrightarrow{AD}\) .

Find the projection of:
(i) \(\hat { i } -\hat { j } \) on Z-axis
(ii) \(\hat { i } +2\hat { j } -2\hat { k } \) on \(2\hat { i } -\hat { \quad j } -2\hat { k } \)
(iii) \(3\hat { i } +\hat { j } -\hat { k } \) on \(4\hat { i } -\hat { j } +2\hat { k } \)

Let \(\overrightarrow { a } ,\overrightarrow { b } \) and \(\overrightarrow { c } \) be unit vectors such that \(\overrightarrow { a } \) is perpendicular to both \(\overrightarrow { b } \) and \(\overrightarrow { c } \) and further the angle between \(\overrightarrow { b } \) and \(\overrightarrow { c } \) is \(\frac { \pi }{ 6 } \). Then \(\overrightarrow { a } =\pm 2\left( \overrightarrow { b } \times \overrightarrow { c } \right) \)

Find the unit vector parallel to 3\(\overrightarrow{a}\) − 2\(\overrightarrow{b}\) + 4\(\overrightarrow{c}\) if \(\overrightarrow{a}\) = 3\(\hat{i}\)−\(\hat{j}\)− 4\(\hat{k}\), \(\overrightarrow{b}\) = −2\(\hat{i}\)+ 4\(\hat{j}\)− 3\(\hat{k}\), and \(\overrightarrow{c}\) =\(\hat{i}\)+ 2\(\hat{j}\)−\(\hat{k}\).

The position vectors of the points P, Q, R, S are \(\hat{i}\) + \(\hat{j}\) + \(\hat{k}\),2 \(\hat{i}\)+5\(\hat{j}\),3\(\hat{i}\)+2\(\hat{j}\)-3\(\hat{k}\), and \(\hat{i}\)-6\(\hat{j}\)-\(\hat{k}\), respectively. Prove that the line PQ and RS are parallel.

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

Show that the points (2, - 1, 3), (4, 3, 1) and (3, 1, 2) are collinear.

If ABCD is a quadrilateral and E and F are the midpoints of AC and BD respectively, then prove that \(\overrightarrow{AB}\) + \(\overrightarrow{AD}\) +\(\overrightarrow{CB}\)+\(\overrightarrow{CD}\) = 4\(\overrightarrow{EF}\).

The position vectors \(\overrightarrow{a}\),\(\overrightarrow{b}\), \(\overrightarrow{c}\) of three points satisfy the relation 2\(\overrightarrow{a}\)-7\(\overrightarrow{b}\) 5\(\overrightarrow{c}\) =\(\overrightarrow{0}\) .Are these points collinear?

Find \(\lambda\), when the projection of \(\overrightarrow{a}=\lambda \hat{i}+\hat{j}+4\hat{k}\) on \(\overrightarrow{b}=2\hat{i}+6\hat{j}+3\hat{k}\) is 4 units.

Let P, Q, R and S be points with position. vectors\(3\hat{i}-2\hat{j}-\hat{k},2\hat{i}+3\hat{j}-4\hat{k},-\hat{i}+\hat{j}+2\hat{k}\) and \(4\hat{i}+5\hat{j}+r\hat{k}\). Find the value of it so that P, Q, Rand S are co-planar.

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

Comment

Add Comment

InstaQB

Institutions

12th Standard English Medium

12th Standard Tamil Medium

11th Standard English Medium

11th Standard Tamil Medium

10th Standard English Medium

9th Standard English Medium

8th Standard English Medium

7th Standard English Medium

Class XII

Class XI

12Th Standard

11Th Standard

10Th Standard

9Th Standard

11th Maths Monthly Test - 4 ( Vector Algebra )

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test - 4 ( Vector Algebra )-Aug 2020

Part - A

Generic 5 - Answer All Question

If D is the midpoint of the side BC of a triangle ABC, prove that \(\overrightarrow{AB}\) + \(\overrightarrow{AC}\) = 2\(\overrightarrow{AD}\) .

Find the projection of: (i) \(\hat { i } -\hat { j } \) on Z-axis (ii) \(\hat { i } +2\hat { j } -2\hat { k } \) on \(2\hat { i } -\hat { \quad j } -2\hat { k } \) (iii) \(3\hat { i } +\hat { j } -\hat { k } \) on \(4\hat { i } -\hat { j } +2\hat { k } \)

The position vectors of the points P, Q, R, S are \(\hat{i}\) + \(\hat{j}\) + \(\hat{k}\),2 \(\hat{i}\)+5\(\hat{j}\),3\(\hat{i}\)+2\(\hat{j}\)-3\(\hat{k}\), and \(\hat{i}\)-6\(\hat{j}\)-\(\hat{k}\), respectively. Prove that the line PQ and RS are parallel.

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

Show that the points (2, - 1, 3), (4, 3, 1) and (3, 1, 2) are collinear.

If ABCD is a quadrilateral and E and F are the midpoints of AC and BD respectively, then prove that \(\overrightarrow{AB}\) + \(\overrightarrow{AD}\) +\(\overrightarrow{CB}\)+\(\overrightarrow{CD}\) = 4\(\overrightarrow{EF}\).

The position vectors \(\overrightarrow{a}\),\(\overrightarrow{b}\), \(\overrightarrow{c}\) of three points satisfy the relation 2\(\overrightarrow{a}\)-7\(\overrightarrow{b}\) 5\(\overrightarrow{c}\) =\(\overrightarrow{0}\) .Are these points collinear?

Find \(\lambda\), when the projection of \(\overrightarrow{a}=\lambda \hat{i}+\hat{j}+4\hat{k}\) on \(\overrightarrow{b}=2\hat{i}+6\hat{j}+3\hat{k}\) is 4 units.

Let P, Q, R and S be points with position. vectors\(3\hat{i}-2\hat{j}-\hat{k},2\hat{i}+3\hat{j}-4\hat{k},-\hat{i}+\hat{j}+2\hat{k}\) and \(4\hat{i}+5\hat{j}+r\hat{k}\). Find the value of it so that P, Q, Rand S are co-planar.

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

Comment

Other Study material

11th Maths Monthly Test -2( Differential Calculus

11th Maths Monthly Test - 4 ( Introduction to prob

11th Maths Weekly Test - 1 ( Differential Calculus

11th Maths Monthly Test - 4 ( Differential Calcul

11th Maths Monthly Test - 3( Differential Calculu

11th Maths Weekly Test - 3 ( Vector Algebra )

11th Maths Weekly Test -4 ( Vector Algebra )

11th Maths Monthly Test- 1 (Vector Algebra )

11th Maths Monthly Test -2( Vector Algebra )

11th Maths Monthly Test - 3 ( Vector Algebra )

11th Maths Monthly Test - 4 ( Vector Algebra )

11th Maths Weekly Test -1( Differential Calculus

11th Maths Weekly Test-2 ( Differential Calculus -

11th Maths Weekly Test - 3 ( Differential Calculus

11th Maths Weekly Test - 4 ( Differential Calculus

Tamilnadu Stateboardszs - Class

Find the projection of:
(i) \(\hat { i } -\hat { j } \) on Z-axis
(ii) \(\hat { i } +2\hat { j } -2\hat { k } \) on \(2\hat { i } -\hat { \quad j } -2\hat { k } \)
(iii) \(3\hat { i } +\hat { j } -\hat { k } \) on \(4\hat { i } -\hat { j } +2\hat { k } \)