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.