Question

Given the magnitude of vector A to be 6 units. Find the component of A along the x-axis?

• A. $3\sqrt{3}$
• B. $3\sqrt{3}\hat{i}$
• C. $-3\sqrt{3}$
• D. $-3\sqrt{3}\hat{i}$

Answer 1

The correct option is C

$-3\sqrt{3}$

Well normally I guess by now you know how to find component of a vector along a given vector i.e.

(Magnitude of vector)×(cosine of angle between the two vectors)

This takes care of everything

$\Rightarrow$ In this case

$6\times cos{150}^{\circ }=6\times cos(90+60)$

= -$6sin{60}^{\circ }=-6\times \frac{\sqrt{3}}{2}=-3\sqrt{3}$

Caution:- Component of a vector is scalar. I agree it's tough to understand and remember trigonometric

identities intuitively. Also component of a vector is just the measure of the shadow

$\Rightarrow$

Here the length of shadow is $6cos{30}^{\circ }=6\times \frac{3}{2}=3\sqrt{3}$ but this component is on -ve x-axis.

But since the question asks the component along the direction of +ve x-axis, so the component should be $-3\sqrt{3}$