For unit vectors b and c and any nonzero vector a the value of abacbcbc is

EASY

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 15 - Vector Algebra>Exercise 2>Q 11

If

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

and

\vec{c} = 3 \hat{i} - \hat{k}

represent three coterminous edges of a parallelepiped, then the volume of that parallelepiped is

HARD

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 15 - Vector Algebra>Exercise 2>Q 12

Three non-coplanar vectors

\vec{a}, \vec{b}

and

\vec{c}

are drawn from a common initial point. The angle between the plane passing through the terminal points of these vectors and the vector

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

is

MEDIUM

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 15 - Vector Algebra>Exercise 2>Q 13

Force

\hat{i} + 2 \hat{j} - 3 \hat{k}, 2 \hat{i} + 3 \hat{j} + 4 \hat{k}

and

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

are acting at the point

P (0, 1, 2)

. The moment of these forces about the point

A (1, - 2, 0)

is

HARD

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 15 - Vector Algebra>Exercise 2>Q 14

If

\vec{a}, \vec{b}

and

\vec{c}

are unit vectors, then

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

does not exceed

HARD

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 15 - Vector Algebra>Exercise 2>Q 15

If

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

and

\vec{c} = 7 \hat{i} + 9 \hat{j} + 11 \hat{k}

, then the area of parallelogram having diagonals

\vec{a} + \vec{b}

and

\vec{b} + \vec{c}

is

MEDIUM

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 15 - Vector Algebra>Exercise 2>Q 16

X

-component of

\vec{a}

is twice its

Y

-component. If the magnitude of the vector is

5 \sqrt{2}

and it makes an angle of

135 °

with

z

-axis then the vector is

MEDIUM

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 15 - Vector Algebra>Exercise 2>Q 17

Forces

3 \hat{i} + 2 \hat{j} + 5 \hat{k}

and

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

are acting at a particle which is displaced from point

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

to the point

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

. The work done by forces is

MEDIUM

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 15 - Vector Algebra>Exercise 2>Q 18

If

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

and

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

, then correct statement is

For unit vectors $\vec{b}$ and $\vec{c}$ and any non-zero vector $\vec{a}$ , the value of $\{(\vec{a} + \vec{b}) \times (\vec{a} + \vec{c})} \times (\vec{b} \times \vec{c})\} \cdot (\vec{b} + \vec{c})$ is

Important Questions on Vector Algebra

Learn and Prepare for any exam you want !

For unit vectors b→ and c→ and any non-zero vector a→, the value of a→+b→×a→+c→}×b→×c→·b→+c→ is

Important Questions on Vector Algebra

Learn and Prepare for any exam you want !

For unit vectors $\vec{b}$ and $\vec{c}$ and any non-zero vector $\vec{a}$ , the value of $\{(\vec{a} + \vec{b}) \times (\vec{a} + \vec{c})} \times (\vec{b} \times \vec{c})\} \cdot (\vec{b} + \vec{c})$ is