Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Vectors>EXERCISE>Q 23

EASY

12th ICSE

IMPORTANT

Earn 100

Find the direction cosines of the vector $\hat{i} + 2 \hat{j} + 3 \hat{k}$ .

Important Questions on Vectors

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Vectors>EXERCISE>Q 23

If

P (1, 5, 4)

and

Q (4, 1, - 2)

, then find the direction ratios of

\vec{P Q}

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Vectors>EXERCISE>Q 23

Find the direction cosines of the vector joining the points

A (1, 2, - 3)

and

B (- 1, - 2, 1)

, directed from

A

to

B

.

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Vectors>EXERCISE>Q 23

What is the cosine of the angle which the vector

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

makes with

y

-axis?

MEDIUM

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Vectors>EXERCISE>Q 24

Find the mid-point of the vector joining the points

P

and

Q

having position vectors

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

and

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

respectively.

MEDIUM

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Vectors>EXERCISE>Q 24

Write the position vector of the point dividing the line segment joining the points with position vectors

\vec{a}

and

\vec{b}

externally in the ratio

1 : 4

, where

\vec{a} = 2 \hat{i} + 3 \hat{j} + 4 \hat{k}

and

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

MEDIUM

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Vectors>EXERCISE>Q 26

Find the position vector of a point

R

which divides the line segment joining the points

P

and

Q

with position vectors

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

and

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

respectively, internally in the ratio

2 : 1

.

MEDIUM

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Vectors>EXERCISE>Q 26

Find the position vector of a point

R

which divides the line segment joining the points

P

and

Q

with position vectors

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

and

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

respectively, externally in the ratio

2 : 1

.

MEDIUM

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Vectors>EXERCISE>Q 27

A

and

B

are two points with position vectors

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

and

6 \vec{b} - \vec{a}

respectively. Write the position vector of a point

P

which divides the line segment

A B

internally in the ratio

1 : 2

.