RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.1

RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.1 are part of RBSE Solutions for Class 12 Maths. Here we have given Rajasthan Board RBSE Class 12 Maths Chapter 13 Vector Ex 13.1.

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 [latex]\widehat { i }[/latex] + 3 [latex]\widehat { j }[/latex] and x [latex]\widehat { i }[/latex] + y [latex]\widehat { j }[/latex] 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 [latex]\widehat { a }[/latex] = [latex]\widehat { i }[/latex] + [latex]\widehat { j }[/latex] + 2 [latex]\widehat { k }[/latex]
Solution:

Question 8.
Find the unit vector in the direction of vector [latex]\overrightarrow { PQ } [/latex] 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 [latex]\overrightarrow { a } +\overrightarrow { b } [/latex]
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.

RBSE Solutions for Class 12 Maths