Figure shows the orientation of two vectors ` vec u` and `vec v` in the (XY) plane.
If ` vec u = a hat i + b hat j` and ` vec v = p hat i+ q hat j` which of the following is correct ?
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Option 1 a and p are positive while b and q are negative
Option 2 a,p and b are positive while q is negative
Option 3 a, q and b are positive while p is negative
Option 4 a, b, p and q are all positive

Options

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

B

Explanation

Clearly from the diagram, `u=a hat(i) + b hat(j)`
As u is in the first quadrant, hence both components a and b will be positive.
For `v=p hat(i) + q hat (j)`, as it is in positive x-direction and located downward hence x-component p will be positive and y-component q will be negative.