Let α ∈ R and the three vectors a → = α i ^ + j ^ + 3 k ^ , b → = 2 i ^ + j ^ - α k ^ and c → = α i ^ - 2 j ^ + 3 k ^ . Then the set S = { α : a → , b → and c → are coplanar}

contains exactly two positive numbers

contains exactly two numbers only one of which is positive

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 →

E M B I B E

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 12th April 2019 Shift 2>Q 65

EASY

JEE Main

IMPORTANT

Earn 100

Let $α \in R$ and the three vectors $\vec{a} = α \hat{i} + \hat{j} + 3 \hat{k}, \vec{b} = 2 \hat{i} + \hat{j} - α \hat{k}$ and $\vec{c} = α \hat{i} - 2 \hat{j} + 3 \hat{k} .$ Then the set S = { $α : \vec{a}, \vec{b}$ and $\vec{c}$ are coplanar}

100% studentsanswered this correctly

Important Questions on Vector Algebra

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 12th January 2019 Shift 1>Q 66

The sum of the distinct real values of

μ

for which the vectors

μ \hat{i} + \hat{j} + \hat{k}, \hat{i} + μ \hat{j} + \hat{k}, \hat{i} + \hat{j} + μ \hat{k}

are co-planar, is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 12th January 2019 Shift 2>Q 67

Let

S

be the set of all real values of

λ

such that a plane passing through the points

(- λ^{2}, 1, 1), (1, - λ^{2}, 1)

and

(1, 1, - λ^{2})

also passes through the point

(- 1, - 1, 1)

. Then

S

is equal to :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 12th January 2019 Shift 2>Q 68

Let

\vec{a}, \vec{b}

and

\vec{c}

be three unit vectors, out of which vectors

\vec{b}

and

\vec{c}

are non-parallel. If

α

and

β

are the angles which vector

\vec{a}

makes with vectors

\vec{b}

and

\vec{c}

respectively and

\vec{a} \times (\vec{b} \times \vec{c}) = \frac{1}{2} \vec{b}

, then

|α - β|

is equal to :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 8th April 2018>Q 69

Let

\vec{u}

be a vector coplanar with the vectors

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

and

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

. If

\vec{u}

is perpendicular to

\vec{a}

and

\vec{u} \cdot \vec{b} = 24

, then

{|\vec{u}|}^{2}

is equal to:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 15th April 2018>Q 70

If

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

are unit vectors such that

\vec{a} + 2 \vec{b} + 2 \vec{c} = \vec{0}

, then

|\vec{a} \times \vec{c}|

is equal to :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 16th April 2018>Q 71

Let

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

and a vector

\vec{b}

be such that

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

and

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

. Then

|\vec{b}|

equals

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Vector Algebra>JEE Main - 2nd April 2017>Q 72

Given, $\vec{a} = 2 \hat{i} + \hat{j} - 2 \hat{k}$ and $\vec{b} = \hat{i} + \hat{j} .$ Let $\vec{c}$ be a vector such that $|\vec{c} - \vec{a}| = 3, |(\vec{a} \times \vec{b}) \times \vec{c}| = 3$ and the angle between $\vec{c}$ and $\vec{a} \times \vec{b}$ be $30 °$ . Then $\vec{a} \cdot \vec{c}$ is equal to: