EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main 18 March 2021 Shift 1>Q 30

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IMPORTANT

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A vector $\vec{a}$ has components $3 p$ and $1$ with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If, with respect to new system, $\vec{a}$ has components $p + 1$ and $\sqrt{10},$ then a value of $p$ is equal to:

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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 18 March 2021 Shift 2>Q 31

In a triangle

A B C

, if

| \vec{B C} | = 8, | \vec{C A} | = 7, | \vec{A B} | = 10

, then the projection of the vector

\vec{A B}

on

\vec{A C}

is equal to :

MEDIUM

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main 18 March 2021 Shift 2>Q 32

Let

\vec{a}

and

\vec{b}

be two non-zero vectors perpendicular to each other and

| \vec{a} | = | \vec{b} |

, If

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

, then the angle between the vectors

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

and

\vec{a}

is equal to :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 24 Feb 2021 Shift 1>Q 33

Let three vectors

\vec{a}, \vec{b}

and

\vec{c}

be such that

\vec{c}

is coplanar with

\vec{a}

and

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

and

\vec{b}

is perpendicular to

\vec{c},

where

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

and

\vec{b} = 2 \hat{i} + \hat{k},

then the value of

2 {|\vec{a} + \vec{b} + \vec{c}|}^{2}

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 25 Feb 2021 Shift 1>Q 34

Let

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

and

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

be three given vectors. If

\vec{r}

is a vector such that

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

and

\vec{r} \cdot \vec{b} = 0,

then

\vec{r} \cdot \vec{a}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 25 Feb 2021 Shift 2>Q 35

Let

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

and

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

. If the area of the parallelogram whose adjacent sides are represented by the vectors

\vec{a}

and

\vec{b}

is

8 \sqrt{3}

square units, then

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

is equal to ___ .

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 26 Feb 2021 Shift 1>Q 36

If

\vec{a}

and

\vec{b}

are perpendicular, then

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

is equal to:

MEDIUM

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 26 Feb 2021 Shift 1>Q 37

If

(1, 5, 35), (7, 5, 5), (1, λ, 7)

and

(2 λ, 1, 2)

are coplanar, then the sum of all possible values of

λ

is:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 26 Feb 2021 Shift 2>Q 38

If vectors

\vec{a_{1}} = x \hat{i} - \hat{j} + \hat{k}

and

\vec{a_{2}} = \hat{i} + y \hat{j} + z \hat{k}

are collinear, then a possible unit vector parallel to the vector

x \hat{i} + y \hat{j} + z \hat{k}

is: