Let a → = 5 i ^ - j ^ - 3 k ^ and b → = i ^ + 3 j ^ + 5 k ^ be two vectors. Then which one of the following statements is TRUE?

Projection of a → on b → is - 13 35 and the direction of the projection vector is opposite to the direction of b →

Projection of a → on b → is - 17 35 and the direction of the projection vector is opposite to the direction of b →

Projection of a → on b → is 17 35 and the direction of the projection vector is opposite to the direction of b →

Projection of a → on b → is 13 35 and the direction of the projection vector is opposite to the direction of a →

HARD

JEE Main

IMPORTANT

Earn 100

Let $\vec{a}, \vec{b}, \vec{c}$ be three coplanar concurrent vectors such that angles between any two of them is same. If the product of their magnitudes is $14$ and $(\vec{a} \times \vec{b}) \cdot (\vec{b} \times \vec{c}) + (\vec{b} \times \vec{c}) \cdot (\vec{c} \times \vec{a}) + (\vec{c} \times \vec{a}) \cdot (\vec{a} \times \vec{b}) = 168$ , then $|\vec{a}| + |\vec{b}| + |\vec{c}|$ is equal to

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Important Questions on Vector Algebra

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 29 July 2022 Shift 2>Q 120

Let

\vec{a}

and

\vec{b}

be two vectors such that

{|\vec{a} + \vec{b}|}^{2} = {|\vec{a}|}^{2} + 2 {|\vec{b}|}^{2}, \vec{a} \cdot \vec{b} = 3

and

{|\vec{a} \times \vec{b}|}^{2} = 75

. Then

{|\vec{a}|}^{2}

is equal to ______.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 24 January 2023 Shift 1>Q 121

Let

\vec{u} = \hat{i} - \hat{j} - 2 \hat{k}, \vec{v} = 2 \hat{i} + \hat{j} - \hat{k}

\vec{v} \cdot \vec{w} = 2

and

\vec{v} \times \vec{w} = \vec{u} + λ \vec{v}

, then

\vec{u} \cdot \vec{w}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 24 January 2023 Shift 1>Q 122

Let

P Q R

be a triangle. The points

A, B

and

C

are on the sides

Q R, R P

and

P Q

respectively such that

\frac{Q A}{A R} = \frac{R B}{B P} = \frac{P C}{C Q} = \frac{1}{2}

. Then

\frac{Area (∆ P Q R)}{Area (∆ A B C)}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 24 January 2023 Shift 2>Q 123

Let

\vec{α} = 4 \hat{i} + 3 \hat{j} + 5 \hat{k}

and

\vec{β} = \hat{i} + 2 \hat{j} - 4 \hat{k}

. Let

{\vec{β}}_{1}

be parallel to

\vec{α}

and

{\vec{β}}_{2}

be perpendicular to

\vec{α}

. If

\vec{β} = {\vec{β}}_{1} + {\vec{β}}_{2}

, then the value of

5 {\vec{β}}_{2} \cdot (\hat{i} + \hat{j} + \hat{k})

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 24 January 2023 Shift 2>Q 124

Let

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

\vec{b} = 3 \hat{i} - 5 \hat{j} - λ \hat{k}

\vec{a} \cdot \vec{c} = 7

2 (\vec{b} \cdot \vec{c}) + 43 = 0

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

, then

\vec{a} \cdot \vec{b}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 25 January 2023 Shift 1>Q 125

Let

\vec{a}, \vec{b}

and

\vec{c}

be three non zero vectors such that

\vec{b} \cdot \vec{c} = 0

and

\vec{a} \times (\vec{b} \times \vec{c}) = \frac{\vec{b} - \vec{c}}{2}

. If

\vec{d}

be a vector such that

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

, then

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

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 25 January 2023 Shift 1>Q 126

The vector

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

is rotated through a right angle, passing through the

y

-axis in its way and the resulting vector is

\vec{b}

. Then the projection of

3 \vec{a} + \sqrt{2} \vec{b}

\vec{c} = 5 \hat{i} + 4 \hat{j} + 3 \hat{k}

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 25 January 2023 Shift 2>Q 127

If the four points, whose position vectors are

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

and

5 \hat{i} - 2 α \hat{j} + 4 \hat{k}

are coplanar, then

α

is equal to

Let a→,b→,c→ be three coplanar concurrent vectors such that angles between any two of them is same. If the product of their magnitudes is 14 and a→×b→·b→×c→+b→×c→·c→×a→+c→×a→·a→×b→=168, then a→+b→+c→ is equal to

Important Questions on Vector Algebra

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