Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 22

EASY

JEE Advanced

IMPORTANT

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If in the given figure, $\vec{O A} = \vec{a}, \vec{O B} = \vec{b}$ and $\vec{A P} : \vec{P B} = m : n$ , then $\vec{O P}$ is equal to

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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 23

If

\vec{a}

and

\vec{b}

are position vector of two points

A, B

and

C

divides

\vec{A B}

in ratio

2 : 1

, then position vector of

C

is

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 24

The position vector of the points which divides internally in the ratio

2 : 3

the join of the points

(2 \vec{a} - 3 \vec{b})

and

(3 \vec{a} - 2 \vec{b})

, is

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 25

If

O

is origin and

C

is the mid-point of

A (2, - 1)

and

B (- 4, 3)

. Then, value of

\vec{O C}

is

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 26

If the position vectors of the points

\vec{A}

and

\vec{B}

are

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

and

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

, then what will be the position vector of the midpoint of

\vec{A B}

.

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 27

The position vectors of

\vec{A}

and

\vec{B}

are

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

and

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

. The position vector of the middle point of the line

\vec{A B}

is

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 28

If the vector

b

is collinear with the vector $a = (2 \sqrt{2}, - 1, 4)$ and

|\vec{b}| = 10

, then

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 29

If

\vec{a} = (1, - 1)

and

\vec{b} = (- 2, m)

are two collinear vectors, then

m

is equal to

EASY

JEE Advanced

IMPORTANT

Skills in Mathematics for JEE MAIN & ADVANCED VECTORS & 3D GEOMETRY>Chapter 1 - Vector Algebra>Vector Algebra Exercise 1>Q 30

The points with position vectors

10 \hat{i} + 3 \hat{j}

,

12 \hat{i} - 5 \hat{j}

and

a \hat{i} + 11 \hat{j}

are collinear, if

a

is equal to