RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.1

Rajasthan Board RBSE Class 12 Maths Chapter 13 Vector Ex 13.1

RBSE Solutions For Class 12 Maths Chapter 13 Question 1.
Compute the magnitude of the following vectors :
RBSE Solutions For Class 12 Maths Chapter 13
Solution:
RBSE Solutions For Class 12 Maths Chapter 13.1
RBSE Class 12 Maths Chapter 13

RBSE Solutions For Class 12 Maths Chapter 13.1 Question 2.
Write two different vectors having same magnitude.
Solution:
Exercise 13.1 Class 12 RBSE Solutions

RBSE Class 12 Maths Chapter 13 Question 3.
Write two different vectors having same direction.
Solution:
12 Maths RBSE Solution Ch 13
Ex 13.1 Class 10 RBSE Ch 13

Exercise 13.1 Class 12 Question 4.
Find the values of x and y so that the vectors 2 \(\widehat { i }\) + 3 \(\widehat { j }\) and x \(\widehat { i }\) + y \(\widehat { j }\) are equal.
Solution:
Two vectors are equal if their corresponding coefficients are equal
12th Maths RBSE Solution Ch 13
⇒ 2 = x and 3 = y
x = 2 and y = 3.

12 Maths RBSE Solution 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
RBSE Solution Class 12 Maths Ch 13

Ex 13.1 Class 10 RBSE Question 6.
RBSE Solutions For Class 10 Maths Chapter 13.1
Solution:
Class 12 Chapter 13 Exercise 13.1 RBSE Solutions
Class 12 Maths Chapter 13 Exercise 13.1 RBSE Solutions

12th Maths RBSE Solution Question 7.
Find the unit vector in the direction of the vector \(\widehat { a }\) = \(\widehat { i }\) + \(\widehat { j }\) + 2 \(\widehat { k }\)
Solution:
Maths Class 12 RBSE Solution Ch 13

RBSE Solution Class 12 Maths Question 8.
Find the unit vector in the direction of vector \(\overrightarrow { PQ } \) where P and Q are the points (1,2,3) and (4,5,6).
Solution:
Ch 13 Maths Class 12 RBSE Solutions
Class 12 Maths RBSE Solutions Ch 13

RBSE Solutions For Class 10 Maths Chapter 13.1 Question 9.
For the given vectors,
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.1
and
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.1
Find the unit vector in the direction of the vector \(\overrightarrow { a } +\overrightarrow { b } \)
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.1

Class 12 Chapter 13 Exercise 13.1 Question 10.
Find a vector in the direction of vector
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.1
which has magnitude 8 units.
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.1

Class 12 Maths Chapter 13 Exercise 13.1 Question 11.
Show that the vectors
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.1
and are collinear.
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.1
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.1

Maths Class 12 RBSE Question 12.
Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.1
and
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.1
respectively in the ratio 2:1.
(i) internally (ii) externally.
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.1
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.1

Ch 13 Maths Class 12 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:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.1

Class 12 Maths RBSE Solutions Question 14.
Show that the points A, B and C with position vectors,
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.1
and
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.1
respectively from the vertices of a right angled triangle.
Solution:
Let O is the origin, then according to question,
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.1
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.1
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.1
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.1
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