Ncert Exercises & Solutions

The figure shows the orientation of two vectors \(u\) and \(v\) in the XY plane.
If \(u=a\hat{i}+b\hat{j}\) and \(v=p\hat{i}+q\hat{j}\).

Which of the following is correct?

1.	\(a\) and \(p\) are positive while \(b\) and \(q\) are negative.
2.	\(a,\) \(p\) and \(b\) are positive while \(q\) is negative.
3.	\(a,\) \(q\) and \(b\) are positive while \(p\) is negative.
4.	\(a,\) \(b,\) \(p\) and \(q\) are all positive.

(b) Hint: We can resolve the vectors along the coordinate axis.

Step 1: Find the direction of u.

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.

Step 2: Find the direction of v.
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.