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}

$u = a \hat{i} + b \hat{j}$
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}

$v = p \hat{i} + q \hat{j}$ . as it is in positive x-direction and located downward hence x-Component p will be positive and y-component q will be negative.

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