## Rajasthan Board RBSE Class 12 Maths Chapter 13 Vector Ex 13.1

Question 1.

Compute the magnitude of the following vectors :

Solution:

Question 2.

Write two different vectors having same magnitude.

Solution:

Question 3.

Write two different vectors having same direction.

Solution:

Question 4.

Find the values of x and y so that the vectors 2 + 3 and x + y are equal.

Solution:

Two vectors are equal if their corresponding coefficients are equal

⇒ 2 = x and 3 = y

x = 2 and y = 3.

Question 5.

Find the scalar and vector components of the vector with initial point (2,1) and terminal point (- 5,7).

Solution:

Coordinates of initial point A are (2, 1).

and coordinates of terminal point B are (- 5, 7)

Now from formula

Question 6.

Solution:

Question 7.

Find the unit vector in the direction of the vector = + + 2

Solution:

Question 8.

Find the unit vector in the direction of vector where P and Q are the points (1,2,3) and (4,5,6).

Solution:

Question 9.

For the given vectors,

and

Find the unit vector in the direction of the vector

Solution:

Question 10.

Find a vector in the direction of vector

which has magnitude 8 units.

Solution:

Question 11.

Show that the vectors

and are collinear.

Solution:

Question 12.

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are

and

respectively in the ratio 2:1.

(i) internally (ii) externally.

Solution:

Question 13.

Find the position vector of the midpoint of the vector joining the points P(2,3,4) and Q(4, 1, -2).

Solution:

Question 14.

Show that the points A, B and C with position vectors,

and

respectively from the vertices of a right angled triangle.

Solution:

Let O is the origin, then according to question,

Hence ∆ABC is a right angled triangle,

or point A, B and C are the vertices of a right angled triangle.

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