MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>VERY SHORT ANSWER QUESTIONS (VSAQs)>Q 39

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If $\vec{a}$ and $\vec{b}$ are perpendicular vectors, $|\vec{a} + \vec{b}| = 13$ and $|\vec{a}| = 5$ find the value of $|\vec{b}|$

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Important Questions on Scalar or Dot Product

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12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>VERY SHORT ANSWER QUESTIONS (VSAQs)>Q 40

If the vectors

\vec{a}

and

\vec{b}

are such that

|\vec{a}| = 3, |\vec{b}| = \frac{2}{3}

and

\vec{a} \times \vec{b}

is a unit vector, then write the angle between

\vec{a}

and

\vec{b}

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12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>VERY SHORT ANSWER QUESTIONS (VSAQs)>Q 41

If

\vec{a}

and

\vec{b}

are two unit vectors such that

\vec{a} + \vec{b}

is also a unit vector, then find the value of

k

, if the angle between

\vec{a}

and

\vec{b}

is

\frac{k π}{3}

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12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>VERY SHORT ANSWER QUESTIONS (VSAQs)>Q 42

If

\vec{a}

and

\vec{b}

are unit vectors, then find the value of

k

, if the angle between

\vec{a}

and

\vec{b}

is

\frac{π}{k}

, given that

(\sqrt{3} \vec{a} - \vec{b})

is a unit vector.

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MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>VERY SHORT ANSWER QUESTIONS (VSAQs)>Q 43

Find the magnitude of each of the two vectors

\vec{a}

and

\vec{b}

, having the same magnitude such that the angle between them is

60 °

and their scalar product is

\frac{9}{2}

.

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12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>MULTIPLE CHOICE QUESTIONS (MCQs)>Q 1

The vectors

\vec{a}

and

\vec{b}

satisfy the equations

2 \vec{a} + \vec{b} = \vec{p}

and

\vec{a} + 2 \vec{b} = \vec{q}

, where

\vec{p} = \hat{i} + \hat{j}

and

\vec{q} = \hat{i} - \hat{j}

. If

θ

is the angle between

\vec{a}

and

\vec{b}

then

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IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>MULTIPLE CHOICE QUESTIONS (MCQs)>Q 2

If

\vec{a} \cdot \hat{i} = \vec{a} \cdot (\hat{i} + \hat{j}) = \vec{a} \cdot (\hat{i} + \hat{j} + \hat{k}) = 1

, then

\vec{a} =

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IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>MULTIPLE CHOICE QUESTIONS (MCQs)>Q 3

If

\vec{a} + \vec{b} + \vec{c} = \vec{0}, |\vec{a}| = 3, |\vec{b}| = 5, |\vec{c}| = 7

, then the angle between

\vec{a}

and

\vec{b}

is

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12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>MULTIPLE CHOICE QUESTIONS (MCQs)>Q 4

Let

\vec{a}

and

\vec{b}

be two unit vectors and

α

be the angle between them. Then,

\vec{a} + \vec{b}

is a unit vector if