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 →

EASY

JEE Main

IMPORTANT

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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

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Important Questions on Vector Algebra

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 25 January 2023 Shift 2>Q 128

Let

\vec{a} = - \hat{i} - \hat{j} + \hat{k}, \vec{a} \cdot \vec{b} = 1

and

\vec{a} \times \vec{b} = \hat{i} - \hat{j}

. Then

\vec{a} - 6 \vec{b}

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 29 January 2023 Shift 1>Q 129

If the vectors

\vec{a} = λ \hat{i} + μ \hat{j} + 4 \hat{k}, \vec{b} = - 2 \hat{i} + 4 \hat{j} - 2 \hat{k}

and

\vec{c} = 2 \hat{i} + 3 \hat{j} + \hat{k}

are coplanar and the projection of

\vec{a}

on the vector

\vec{b}

\sqrt{54}

units, then the sum of all possible values of

λ + μ

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 29 January 2023 Shift 1>Q 130

Let

\vec{a}, \vec{b}

and

\vec{c}

be three non-zero non-coplanar vectors. Let the position vectors of four points

A, B, C

and

D

\vec{a} - \vec{b} + \vec{c}, λ \vec{a} - 3 \vec{b} + 4 \vec{c}

- \vec{a} + 2 \vec{b} - 3 \vec{c}

and

2 \vec{a} - 4 \vec{b} + 6 \vec{c}

respectively. If

\vec{A B}

\vec{A C}

and

\vec{A D}

are coplanar, then

λ

is :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 29 January 2023 Shift 2>Q 131

\vec{a} = \hat{i} + 2 \hat{k}, \vec{b} = \hat{i} + \hat{j} + \hat{k}, \vec{c} = 7 \hat{i} - 3 \hat{j} + 4 \hat{k}, \vec{r} \times \vec{b} + \vec{b} \times \vec{c} = \vec{0}

and

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

then

\vec{r} . \vec{c}

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 29 January 2023 Shift 2>Q 132

Let

\vec{a} = 4 \hat{i} + 3 \hat{j}

and

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

and

\vec{c}

is a vector such that

\vec{c} \cdot (\vec{a} \times \vec{b}) + 25 = 0, \vec{c} \cdot (\hat{i} + \hat{j} + \hat{k}) = 4

and projection of

\vec{c}

\vec{a}

1

, then the projection of

\vec{c}

\vec{b}

equals:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 30 January 2023 Shift 1>Q 133

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

are three non-zero vectors and

\hat{n}

is a unit vector perpendicular to

\vec{c}

such that

\vec{a} = α \vec{b} - \hat{n}, (α \neq 0)

and

\vec{b} \cdot \vec{c} = 12

, then

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

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 30 January 2023 Shift 2>Q 134

Let $λ \in ℝ, \vec{a} = λ \hat{i} + 2 \hat{j} - 3 \hat{k}, \vec{b} = \hat{i} - λ \hat{j} + 2 \hat{k}$ , If $((\vec{a} + \vec{b}) \times (\vec{a} \times \vec{b})) \times (\vec{a} - \vec{b}) = 8 \hat{i} - 40 \hat{j} - 24 \hat{k}$ then $| λ (\vec{a} + \vec{b}) \times (\vec{a} - \vec{b}) |^{2}$ is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 30 January 2023 Shift 2>Q 135

Let

\vec{a}

and

\vec{b}

be two vectors. Let

| \vec{a} | = 1, | \vec{b} | = 4

and

\vec{a} \cdot \vec{b} = 2

. If

\vec{c} = (2 \vec{a} \times \vec{b}) - 3 \vec{b}

, then the value of

\vec{b} \cdot \vec{c}

If the four points, whose position vectors are 3i^-4j^+2k^,i^+2j^-k^,-2i^-j^+3k^ and 5i^-2αj^+4k^ are coplanar, then α is equal to

Important Questions on Vector Algebra

Learn and Prepare for any exam you want !

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