Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 13

EASY

JEE Advanced

IMPORTANT

Earn 100

The position vectors of $A$ and $B$ are $2 \hat{i} -9 \hat{j} - 4 \hat{k}$ and $6 \hat{i} -3 \hat{j} +8 \hat{k}$ respectively, then the magnitude of $\vec{A B}$ is

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Important Questions on Vector Algebra

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 14

If the position vectors of

P

and

Q

are

(\hat{i} + 3 \hat{j} - 7 \hat{k})

and

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

, then

|\vec{P Q}| =

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 15

If the position vectors of

\vec{P}

and

\vec{Q}

are

\hat{i} +2 \hat{j} - 7 \hat{k}

and

5 \hat{i} - 3 \hat{j} +4 \hat{k}

respectively, the cosine of the angle between

\vec{P Q}

and

Z

- axis is

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 16

If the position vector of

A & B

are

\hat{i} + 3 \hat{j} - 7 \hat{k}

and

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

, then the direction cosine of

A B

along

Y

-axis is

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 17

The direction cosines of vector

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

in the direction of positive axis of

X

is

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 18

The direction cosines of the vector

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

are

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 19

The point having position vectors

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

,

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

and

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

are the vertices of

MEDIUM

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 20

If the position vectors of the vertices

A, B

and

C

of

Δ

A B C

are

7 \hat{j} + 10 \hat{k}

,

- \hat{i} + 6 \hat{j} + 6 \hat{k}

and

- 4 \hat{i} + 9 \hat{j} + 6 \hat{k}

, respectively, then the triangle is

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 21

If

\vec{a}, \vec{b}

and

\vec{c}

are the position vectors of the vertices

A, B

and

C

of the

Δ A B C

, then the centroid of

Δ A B C

is