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 →

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 →

EASY

JEE Main

IMPORTANT

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Let $\vec{a} = 5 \hat{i} - \hat{j} - 3 \hat{k}$ and $\vec{b} = \hat{i} + 3 \hat{j} + 5 \hat{k}$ be two vectors. Then which one of the following statements is TRUE?

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Important Questions on Vector Algebra

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 26 August 2021 Shift 1>Q 1

Let

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

and

\vec{b} = \hat{j} - \hat{k} .

\vec{c}

is a vector such that

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

and

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

, then

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

is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 26 August 2021 Shift 2>Q 2

If the projection of the vector

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

on the sum of the two vectors

2 \hat{i} + 4 \hat{j} - 5 \hat{k}

and

- λ \hat{i} + 2 \hat{j} + 3 \hat{k}

1

, then

λ

is equal to _______.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 27 August 2021 Shift 1>Q 3

Let

\vec{a} = \hat{i} + 5 \hat{j} + α \hat{k}, \vec{b} = \hat{i} + 3 \hat{j} + β \hat{k}

and

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

be three vectors such that,

| \vec{b} \times \vec{c} | = 5 \sqrt{3}

and

\vec{a}

is perpendicular to

\vec{b} .

Then the greatest amongst the values of

| \vec{a} |^{2}

is ________.

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 31 August 2021 Shift 1>Q 4

Let $\vec{a}$ and $\vec{b}$ be two vectors such that $| 2 \vec{a} + 3 \vec{b} | = | 3 \vec{a} + \vec{b} |$ and the angle between $\vec{a}$ and $\vec{b}$ is $60 ° .$ If $\frac{1}{8} \vec{a}$ is a unit vector, then $| \vec{b} |$ is equal to :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 31 August 2021 Shift 2>Q 5

Let

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

be three vectors mutually perpendicular to each other and have same magnitude. If a vector

\vec{r}

satisfies

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

then

\vec{r}

is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 1 September 2021 Shift 2>Q 6

Let

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

and

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

Let a vector

\vec{v}

be in the plane containing

\vec{a}

and

\vec{b} .

\vec{v}

is perpendicular to the vector

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

and its projection on

\vec{a}

19

units, then

| 2 \vec{v} |^{2}

is equal to _____.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 20 July 2021 Shift 1>Q 7

Let

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

and

\vec{b} = \hat{i} + \hat{j}

. If

\vec{c}

is a vector such that

\vec{a} \cdot \vec{c} = | \vec{c} |, | \vec{c} - \vec{a} | = 2 \sqrt{2}

and the angle between

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

and

\vec{c}

\frac{π}{6}

, then the value of

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

is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 20 July 2021 Shift 1>Q 8

Let

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

be three mutually perpendicular vectors of the same magnitude and equally inclined at an angle

θ

, with the vector

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

. Then

36 \cos^{2} 2 θ

is equal to

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

Important Questions on Vector Algebra

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Let $\vec{a} = 5 \hat{i} - \hat{j} - 3 \hat{k}$ and $\vec{b} = \hat{i} + 3 \hat{j} + 5 \hat{k}$ be two vectors. Then which one of the following statements is TRUE?