Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-3>Q 26

HARD

JEE Main/Advance

IMPORTANT

Earn 100

If $\vec{u}$ , $\vec{v}$ and $\vec{w}$ are non-coplanar vectors and $p and q$ are real numbers, then the equality $[3 \vec{u} p \vec{v} p \vec{w}] - [p \vec{v} \vec{w} q \vec{u}] - [2 \vec{w} q \vec{v} q \vec{u}] = 0$ holds for

50% studentsanswered this correctly

Important Questions on Vector Algebra

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-3>Q 27

Let $\vec{a} = \hat{j} - \hat{k}$ and

\vec{c} = \hat{i} - \hat{j} - \hat{k}

. Then the vector

\vec{b}

satisfying

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

and

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

is

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-3>Q 29

If

\vec{a} = \frac{1}{\sqrt{10}} (3 \hat{i} + \hat{k})

and

\vec{b} = \frac{1}{7} (2 \hat{i} + 3 \hat{j} - 6 \hat{k}),

then the value of

(2 \vec{a} - \vec{b}) \cdot [(\bar{a} \times \vec{b}) \times (\vec{a} + 2 \vec{b})]

is

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-3>Q 30

The vectors

\vec{a}

and

\vec{b}

are not perpendicular and

\vec{c}

and

\vec{d}

are two vectors satisfying

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

and

\vec{a} \cdot \vec{d} = 0

. Then, the vector

\vec{d}

is equal to

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-3>Q 31

If the vector

p \hat{i} + \hat{j} + \hat{k}, \hat{i} + q \hat{j} + \hat{k}

and

\hat{i} + \hat{j} + r \hat{k} (p \neq q \neq r \neq 1)

are coplanar, then the value of

p q r - (p + q + r)

is-

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-3>Q 32

If

\vec{a}, \vec{b}

and

\vec{c}

are three non-zero vectors which are pairwise non-collinear. If

\vec{a} + 3 \vec{b}

is collinear with

\vec{c}

and

\vec{b} + 2 \vec{c}

is collinear with

\vec{a}

then

\vec{a} + 3 \vec{b} + 6 \vec{c}

is

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-3>Q 33

Let

\hat{a}

and

\hat{b}

be two unit vectors. If the vectors

\vec{c} = \hat{a} + 2 \hat{b}

and

\vec{d} = 5 \hat{a} - 4 \hat{b}

are perpendicular to each other, then the angle between

\hat{a}

and

\hat{b}

is

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-3>Q 34

Let

A B C D

be a parallelogram such that

\vec{A B} = \vec{q}

,

\vec{A D} = \vec{p}

and

∠ B A D

be an acute angle. If

\vec{r}

is the vector that coincides with the altitude directed from the vertex

B

to the side

A D

, then

\vec{r}

is given by

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 20 - Vector Algebra>Exercise-3>Q 35

The vectors

\vec{A B} = 3 \hat{i} + 4 \hat{k}

and

\vec{A C} = 5 \hat{i} - 2 \hat{j} + 4 \hat{k}

are sides of a triangle

A B C

. The length of the median through

A

is