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 →

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 29 June 2022 Shift 2>Q 101

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IMPORTANT

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Let $A, B, C$ be three points whose position vectors respectively are:

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

$\vec{b} = 2 \hat{i} + α \hat{j} + 4 \hat{k}, α \in R$

$\vec{c} = 3 \hat{i} - 2 \hat{j} + 5 \hat{k}$

If $α$ is the smallest positive integer for which $\vec{a}, \vec{b}, \vec{c}$ are non-collinear, then the length of the median of $△ A B C$ through $A$ is:

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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 June 2022 Shift 2>Q 102

Let

\vec{a} = \hat{i} - 2 \hat{j} + 3 \hat{k}, \vec{b} = \hat{i} + \hat{j} + \hat{k}

and

\vec{c}

be a vector such that

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

, then the value of

3 (\vec{c} . \vec{a})

is equal to _______.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 25 July 2022 Shift 1>Q 103

Let $A B C$ be a triangle such that $\vec{B C} = \vec{a}, \vec{C A} = \vec{b}$ , $\vec{A B} = \vec{c}, |\vec{a}| = 6 \sqrt{2}, |\vec{b}| = 2 \sqrt{3}$ and $\vec{b} \cdot \vec{c} = 12$

Consider the statements :

$(S 1)$ : $|(\vec{a} \times \vec{b}) + (\vec{c} \times \vec{b})| - |\vec{c}| = 6 (2 \sqrt{2} - 1)$

$(S 2)$ : $∠ A C B = \cos^{- 1} (\sqrt{\frac{2}{3}})$ . Then

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 25 July 2022 Shift 2>Q 104

The shortest distance between the lines

\frac{x + 7}{- 6} = \frac{y - 6}{7} = z

and

\frac{7 - x}{2} = y - 2 = z - 6

is

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 25 July 2022 Shift 2>Q 105

Let

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

and let

\vec{b}

be a vector such that

\vec{a} \times \vec{b} = 2 \hat{i} - \hat{k}

and

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

. Then the projection of

\vec{b}

on the

\vec{a} - \vec{b}

is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 26 July 2022 Shift 1>Q 106

Let

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

and

\vec{b} = 2 \hat{i} + \hat{j} - α \hat{k}, α > 0

. If the projection of

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

on the vector

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

is

30

, then

α

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 26 July 2022 Shift 2>Q 107

The plane passing through the line

L : l x - y + 3 (1 - l)

z = 1, x + 2 y - z = 2

and perpendicular to the plane

3 x + 2 y + z = 6

is

3 x - 8 y + 7 z = 4

. If

θ

is the acute angle between the line

L

and the

y

-axis, then

415 \cos^{2} θ

is equal to ______.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 27 July 2022 Shift 1>Q 108

Let

\vec{a} = α \hat{i} + \hat{j} + β \hat{k}

and

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

be two vectors, such that

\vec{a} \times \vec{b} = - \hat{i} + 9 \hat{i} + 12 \hat{k}

. Then the projection of

\vec{b} - 2 \vec{a}

on

\vec{b} + \vec{a}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 27 July 2022 Shift 1>Q 109

Let

\vec{a} = 2 \hat{i} - \hat{j} + 5 \hat{k}

and

\vec{b} = α \hat{i} + β \hat{j} + 2 \hat{k}

. If

((\vec{a} \times \vec{b}) \times \hat{i}) \cdot \hat{k} = \frac{23}{2}

, then

|\vec{b} \times 2 \hat{j}|

is equal to

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Let A, B, C be three points whose position vectors respectively are: a→=i^+4j^+3k^ b→=2i^+αj^+4k^, α∈R c→=3i^-2j^+5k^ If α is the smallest positive integer for which a→, b→, c→ are non-collinear, then the length of the median of △ABC through A is:

Important Questions on Vector Algebra

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