Questions - Answers
Very Short Answer Questions
1. Calculate the dot product of two vectors 
and 
given by 
; 
= 
2. Calculate the work done when a force of 2
+ 5 
+ 5 
acts on a body producing a displacement of 2 + 4 + 6 .
Sol: Work done = 
= 4 + 20 + 30 = 54 Units.
3. Is electric current a vector or a scalar?
Sol: Electric current is a scalar although it has magnitude and direction. Since we cannot meaningfully apply triangle or parallelogram law of vectors.
4. Aboat is moving with a velocity of 3 + 4 with respect to the ground. The water in the river is moving with a velocity of -3 -4 with respect to the ground. Find the relative velocity of the boat with respect to water.
Sol: Velocity of boat = 3 + 4 ; Velocity of river water = -3 -4
Relative velocity of the boat w.r.t water will be
3 + 4 - ( -3 -4 ) = 6 + 8
5. If 
. 
= 0, what is the value of 
?
Sol: . = 0, means 
= AB cos θ = 0
θ = 90º ; = AB sin θ
= AB sin 90º = AB
Short Answer Questions
1. Two vectors of same magnitude have a resultant equal to either. Then what is the angle between the vectors?
Sol: Resultant 
Given P = Q = R.
or 2 (1 + cos θ) = 1 ; (1+cos θ) = ½
or cos θ = -½ ; θ = 120º
2. If = 3 + 4 and = 7 + 24 , find 
, a vector having the same magnitude as and parallel to .
Sol: 
The vector 
should have a magnitude 25 and parallel to . A vector parallel to will be equal to n ( 3 + 4 ) where n is an integer.
When n = 5, the vector will be 5 (3 + 4 ) = 15 + 20
The vector = 15 + 20 has a magnitude of 25.
Since 
Hence the required vector = 15 + 20 .
3. Find the angle between and 
given = 3 + 2 - 6 ; = 4 - 3 +
Sol: . = 
cos θ
The angle between and is 90º i.e., they are perpendicular to each other.
