Question

Figure shows the orientation of two vectors u
and v in the XY plane.
If u = a iˆ + b ˆj and v = p iˆ + q ˆj
which of the following is correct?
(a) a and p are positive while b and q are negative
(b) a, p and b are positive while q is negative
(c) a, q and b are positive while p is negative
(d) a, b, p and q are all positive

Answer 1

Answer:

d , because given vector has positive signs

Answer 2

Answer:

B is the correct answer.

Explanation:

for  

u

, the tail is placed at the origin and both the x-component and y-component have projection on positive x-axis and y-axis respectively. Therefore, a and b are positive. Next, we translate  

v

 in such a way that its direction is unchanged and its tail is placed at the origin. We will observe that the x-component has projection on positive x-axis, whereas, the y-component has projection on the negative y-axis. Therefore, p is positive but q is negative.

Hence, B is the correct answer.