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 :
Solution:
RBSE Solutions For Class 12 Maths Chapter 13.1 Question 2.
Write two different vectors having same magnitude.
Solution:
RBSE Class 12 Maths Chapter 13 Question 3.
Write two different vectors having same direction.
Solution:
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
⇒ 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
Ex 13.1 Class 10 RBSE Question 6.
Solution:
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:
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:
RBSE Solutions For Class 10 Maths Chapter 13.1 Question 9.
For the given vectors,
and
Find the unit vector in the direction of the vector \(\overrightarrow { a } +\overrightarrow { b } \)
Solution:
Class 12 Chapter 13 Exercise 13.1 Question 10.
Find a vector in the direction of vector
which has magnitude 8 units.
Solution:
Class 12 Maths Chapter 13 Exercise 13.1 Question 11.
Show that the vectors
and are collinear.
Solution:
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
and
respectively in the ratio 2:1.
(i) internally (ii) externally.
Solution:
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:
Class 12 Maths RBSE Solutions 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.