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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