NCERT Exemplar Mathematics - Class 12>Chapter 10 - Vector Algebra>EXERCISE>Q 14

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IMPORTANT

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Using vectors, prove that the parallelogram on the same base and between the same parallels are equal in area.

Important Questions on Vector Algebra

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IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 10 - Vector Algebra>EXERCISE>Q 15

Prove that in any triangle

= (\overset{⇀}{a} \times \overset{⇀}{b}) + (\overset{⇀}{a} \times k \overset{⇀}{a})

, where

a, b, c

are the magnitudes of the sides opposite to the vertices

A, B, C

, respectively.

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IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 10 - Vector Algebra>EXERCISE>Q 16

If

\vec{a}, \vec{b}, \vec{c}

determine the vertices of a triangle, show that

\frac{1}{2} [\vec{b} \times \vec{c} + \vec{c} \times \vec{a} + \vec{a} \times \vec{b}]

gives the vector area of the triangle. Hence deduce the condition that the three points

\vec{a}, \vec{b}, \vec{c}

are collinear. Also find the unit vector normal to the plane of the triangle.

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NCERT Exemplar Mathematics - Class 12>Chapter 10 - Vector Algebra>EXERCISE>Q 17

Area of the parallelogram whose diagonals are given by

\vec{a}

and

\vec{b}

is

\frac{| \vec{a} \times \vec{b} |}{m}

. Also the area of the parallelogram whose diagonals are

2 \vec{i} - \hat{j} + \hat{k}

and

\vec{i} - 3 \hat{j} + \hat{k}

is

\frac{1}{2} \sqrt{n}

square units. Find the value of

m + n

?

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NCERT Exemplar Mathematics - Class 12>Chapter 10 - Vector Algebra>EXERCISE>Q 18

If

\vec{a} = \hat{i} + \hat{j} + \hat{k}

and

\vec{b} = \hat{j} - \hat{k}

, magnitude of a vector

|\vec{c}|

is

\sqrt{\frac{x}{y}}

such that

\vec{a} \times \vec{c} = \vec{b}

and

\vec{a} . \vec{c} = 3

, find

x

.

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IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 10 - Vector Algebra>EXERCISE>Q 19

The vector in the direction of the vector

\hat{i} - 2 \hat{j} + 2 \hat{k}

that has magnitude

9

is

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IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 10 - Vector Algebra>EXERCISE>Q 20

The position vector of the point which divides the join of points

2 \vec{a} - 3 \vec{b}

and

\vec{a} + \vec{b}

in the ratio

3 : 1

is

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NCERT Exemplar Mathematics - Class 12>Chapter 10 - Vector Algebra>EXERCISE>Q 21

The vector having initial and terminal points as

(2, 5, 0)

and

(- 3, 7, 4)

respectively is

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IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 10 - Vector Algebra>EXERCISE>Q 22

The angle between two vectors

\vec{a}

and

\vec{b}

of magnitudes

\sqrt{3}

and

4

respectively and

\vec{a} \cdot \vec{b} = 2 \sqrt{3}

is