MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>MULTIPLE CHOICE QUESTIONS (MCQs)>Q 8

MEDIUM

12th CBSE

IMPORTANT

Earn 100

If the vectors $\hat{i} - 2 x \hat{j} + 3 y \hat{k}$ and $\hat{i} + 2 x \hat{j} - 3 y \hat{k}$ are perpendicular, then the locus of $(x, y)$ is

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Important Questions on Scalar or Dot Product

EASY

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>MULTIPLE CHOICE QUESTIONS (MCQs)>Q 9

The vector component of

\vec{b}

perpendicular to

\vec{a}

is

HARD

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>MULTIPLE CHOICE QUESTIONS (MCQs)>Q 10

The length of the longer diagonal of the parallelogram constructed on

5 \vec{a} + 2 \vec{b}

and

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

, if it is given that

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

and the angle between

\vec{a}

and

\vec{b}

is

\frac{π}{4}

?

MEDIUM

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>MULTIPLE CHOICE QUESTIONS (MCQs)>Q 11

If θ is the angle between two vectors

\vec{a}

and

\vec{b}

, then

\vec{a} \cdot \vec{b} \geq 0

only when

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12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>MULTIPLE CHOICE QUESTIONS (MCQs)>Q 13

The values of

x

for which the angle between

\vec{a} = 2 x^{2} \hat{i} + 4 x \hat{j} + \hat{k}, \vec{b} = 7 \hat{i} - 2 \hat{j} + x \hat{k}

is obtuse and the angle between

\vec{b}

and the

z

-axis is acute and less than

\frac{π}{6}

are

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12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>MULTIPLE CHOICE QUESTIONS (MCQs)>Q 14

If

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

are any three mutually perpendicular vectors of equal magnitude, then

|\vec{a} + \vec{b} + \vec{c}|

is equal to

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12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>MULTIPLE CHOICE QUESTIONS (MCQs)>Q 15

If the vectors

3 \hat{i} + λ \hat{j} + \hat{k} and 2 \hat{i} - \hat{j} + 8 \hat{k}

are perpendicular, then

λ

is equal to

MEDIUM

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>MULTIPLE CHOICE QUESTIONS (MCQs)>Q 16

The projection of the vector

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

along the vector of

\hat{j}

is

EASY

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>MULTIPLE CHOICE QUESTIONS (MCQs)>Q 17

The vectors

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

and

a \hat{i} + \hat{b} j + c \hat{k}

are perpendicular if