NCERT Exemplar Mathematics - Class 12>Chapter 10 - Vector Algebra>EXERCISE>Q 7

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12th CBSE

IMPORTANT

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A vector $\vec{r}$ has magnitude $14$ and direction ratios $2, 3, - 6$ . Find the direction cosines and magnitude of the components of $\vec{r}$ , given that $\vec{r}$ makes an acute angle with $x$ -axis.[ Enter the $x$ component of vector $\vec{r}$ ].

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Important Questions on Vector Algebra

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12th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 10 - Vector Algebra>EXERCISE>Q 8

Find a vector of magnitude

6

, which is perpendicular to both the vectors

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

and

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

. (Write the coefficient of

\hat{i}

in the obtained vector respectively).

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12th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 10 - Vector Algebra>EXERCISE>Q 9

The cosine of the angle between the vectors

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

and

3 \hat{i} + 4 \hat{j} - \hat{k}

is of the form

\frac{1}{\sqrt{a}}

, then the value of

a

is

EASY

12th CBSE

IMPORTANT

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

If

\overset{⇀}{a} + \overset{⇀}{b} + \overset{⇀}{c} = 0

, determine whether

\overset{⇀}{a} \times \overset{⇀}{b}, \overset{⇀}{b} \times \overset{⇀}{c} and \overset{⇀}{c} \times \overset{⇀}{a}

are equal or not. Interpret the result geometrically?

EASY

12th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 10 - Vector Algebra>EXERCISE>Q 11

The sine of the angle between the vectors

\overset{⇀}{a} = 3 \hat{i} + \hat{j} + 2 \hat{k}

and

\overset{⇀}{b} = 2 \hat{i} - 2 \hat{j} + 4 \hat{k}

is of the form

\frac{2}{\sqrt{a}}

, then

a =

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12th CBSE

IMPORTANT

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

If

A, B, C, D

are the points with position vectors

\hat{i} + \hat{j} - \hat{k}, 2 \hat{i} - \hat{j} + 3 \hat{k}, 2 \hat{i} - 3 \hat{k}, 3 \hat{i} - 2 \hat{j} + \hat{k}

, respectively, if the projection of

\vec{A B}

along

\vec{C D}

is of the form

\sqrt{a}

, then

a =

EASY

12th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 10 - Vector Algebra>EXERCISE>Q 13

Area of the triangle

A B C

with vertices

A (1, 2, 3), B (2, - 1, 4)

and

C (4, 5, - 1)

is given by

\frac{\sqrt{k}}{2}

sq. units. Find the value of

k

.

EASY

12th CBSE

IMPORTANT

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

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

EASY

12th CBSE

IMPORTANT

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

Prove that in any triangle

ABC, \cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c}

, where

a, b, c

are the magnitudes of the sides opposite to the vertices

A, B, C

, respectively.