Question

Find component of vector $\overrightarrow{A}$ along the direction of $\overrightarrow{B}$ A||B and in perpendicular direction of $\overrightarrow{B}$ $A\perp B$.

• A. A||B = 5; $A\perp B=5\sqrt{3}$
• B. A||B = $5\sqrt{3};A\perp B=5$
• C. A||B = -5; $A\perp B=5\sqrt{3}$
• D. A||B = $5\sqrt{3};A\perp B=-5$

Answer 1

The correct option is C

A||B = -5; $A\perp B=5\sqrt{3}$

So component of A along direction of B is $Acos{120}^{\circ }=-Asin30=-5$

$[\because cos(90+\theta )=-sin\theta ]$

Here we can see if just measure the shadow you will get a $cos60=\frac{a}{2}=5$

But since this 5 is in the opposite direction of vector B so we say that the component of A along the

direction B is -5.

Now component in the perpendicular direction of B is

$Asin\left({120}^{\circ }\right)=Acos30=5\sqrt{3}$

$[\because sin(90+\theta )=cos\theta ]$

Just the shadow measurement is a cos ${30}^{\circ }$ and it's in the perpendicular direction, so no need to

change sign.

So component along the direction is always $acos\theta$ and in perpendicular direction is $asin\theta$. This will take care of sign so don't worry.