NCERT Exemplar Mathematics - Class 12>Chapter 10 - Vector Algebra>EXERCISE>Q 29

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12th CBSE

IMPORTANT

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If $\vec{a}, \vec{b}, \vec{c}$ are unit vectors such that $\vec{a} + \vec{b} + \vec{c} = \vec{0}$ , then the value of $\vec{a} . \vec{b} + \vec{b} . \vec{c} + \vec{c} . \vec{a}$ is

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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 30

Projection vector of

\vec{a}

on

\vec{b}

is

EASY

12th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 10 - Vector Algebra>EXERCISE>Q 31

If

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

are three vectors such that

\vec{a} + \vec{b} + \vec{c} = \vec{0}

and

| \vec{a} | = 2, | \vec{b} | = 3, | \vec{c} | = 5

, then value of

\vec{a} \cdot \vec{b} + \vec{b} . \vec{c} + \vec{c} . \vec{a}

is

EASY

12th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 10 - Vector Algebra>EXERCISE>Q 32

If

| \vec{a} | = 4

and

- 3 \leq λ \leq 2

, then the range of

| λ \vec{a} |

is

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12th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 10 - Vector Algebra>EXERCISE>Q 33

The number of vectors of unit length perpendicular to the vectors

\vec{a} = 2 \hat{i} + \hat{j} + 2 \hat{k}

and

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

is/are

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12th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 10 - Vector Algebra>EXERCISE>Q 34

The vector

\overset{⇀}{a} + \overset{⇀}{b}

bisects the angle between the non-collinear vectors

\overset{⇀}{a}

and

\overset{⇀}{b}

if they are _____ vectors.

EASY

12th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 10 - Vector Algebra>EXERCISE>Q 35

If

\vec{r} \cdot \vec{a} = 0, \vec{r} \cdot \vec{b} = 0

and

\vec{r} . \vec{c} = 0

for some non-zero vector

\vec{r}

, then the value of

\vec{a} \cdot (\vec{b} \times \vec{c})

is _____.

EASY

12th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 10 - Vector Algebra>EXERCISE>Q 36

The vector

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

and

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

are the adjacent sides of a parallelogram. The acute angle between its diagonals is

π \times

_____.

EASY

12th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 10 - Vector Algebra>EXERCISE>Q 37

The values of

k

for which

| k \vec{a} | < | \vec{a} |

and

k \vec{a} + \frac{1}{2} \vec{a}

is parallel to

\vec{a}

and

\vec{a}

is not a null vector holds true are

k \in (m, n)

,

k \neq p

the value of

m + n + p

is _____ .