Two vectors `vec(u)` and `vec(v)` given by `vec(u) = ahat(i)+bhat(j)` and `vec(v)=phat(i) + qhat(j)` have their orientation in the plane XY as shown in the fig. Which of the statements will apply correctly to them.

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', 'p', 'b', 'q' are all positive.

Answer

B

Explanation

For the vector . `vec(u)` ’ both the components along X-axis as well as along Y-axis in the plane X-Y are positive.
Thus both ‘a’ and ‘b’ must be positive. For vector `vec(v)` the component in the X-plane is positive. While that in Y-plane is negative. Thus ‘p’ is positive and ‘g’ is negative. Hence ‘a’, ‘p’ and ‘b’ are positive and are negative