11th Maths Weekly Test -4 ( Vector Algebra )

St. Britto Hr. Sec. School - Madurai

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

Time : 1.30 Hours

Part - A

Generic 3 - Answer All Question

Find the angle A of the triangle whose vertices are A(0, -1, 2), B(3, 1, 4) and C(5, 7, 1).

Prove that the line segments joining the midpoints of the adjacent sides of a quadrilateral form a parallelogram.

If \(\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}\)are position vectors of the vertices A, B, C of a triangle ABC, show that the area of the triangle ABC is \({1\over 2}|\overrightarrow{a}\times \overrightarrow{b}+ \overrightarrow{b}+\overrightarrow{c}+\overrightarrow{c}\times \overrightarrow{a}|\) .Also deduce the condition for collinearity of the points A, B, and C.

Find the area of a triangle having the points A(1,0,0),B(0,1,0), and C(0,0,1) A BC as its vertices.

Find the value of \(\lambda\) for which the vectors \(\overrightarrow{a}=3\hat{i}+2\hat{j}+9\hat{k} \) and \(\overrightarrow{b}=\overrightarrow{i}+\lambda \overrightarrow{j}+3\overrightarrow{k}\) are parallel.

Find the angle between the vectors \(5\hat{i}+3\hat{j}+4\hat{k}\)and\(6\hat{i}-8\hat{j}-\hat{k}\).

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).

If the sum of two unit vectors is a unit vector prove that the magnitude oftheir difference \(\sqrt { 3 } \) is

Show that each of the given three vectors is a unit vector. \(\frac { 1 }{ 7 } (2\hat { i } +3\hat { j } +6\hat { k } );\frac { 1 }{ 7 } (3\hat { i } -6\hat { j } +2\hat { k } );\frac { 1 }{ 7 } (6\hat { i } +2\hat { j } -3\hat { k } )\) Also, show that they are mutually perpendicular to each other.

If \(\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}\)are three vectors such that \(\overrightarrow{a}+2\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}\) and \(|\overrightarrow{a}|=3,|\overrightarrow{b}|=4,|\overrightarrow{c}|=7,\)find the angle between \(\overrightarrow{a}\)and\(\overrightarrow{b}\).

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11th Maths Weekly Test -4 ( Vector Algebra )

St. Britto Hr. Sec. School - Madurai

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

Part - A

Generic 3 - Answer All Question

Find the angle A of the triangle whose vertices are A(0, -1, 2), B(3, 1, 4) and C(5, 7, 1).

Prove that the line segments joining the midpoints of the adjacent sides of a quadrilateral form a parallelogram.

Find the area of a triangle having the points A(1,0,0),B(0,1,0), and C(0,0,1) A BC as its vertices.

Find the value of \(\lambda\) for which the vectors \(\overrightarrow{a}=3\hat{i}+2\hat{j}+9\hat{k} \) and \(\overrightarrow{b}=\overrightarrow{i}+\lambda \overrightarrow{j}+3\overrightarrow{k}\) are parallel.

Find the angle between the vectors \(5\hat{i}+3\hat{j}+4\hat{k}\)and\(6\hat{i}-8\hat{j}-\hat{k}\).

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).

If the sum of two unit vectors is a unit vector prove that the magnitude oftheir difference \(\sqrt { 3 } \) is

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