Question

A watermelon seed has the following coordinates: x=-5.0 m, y=9.0 m and z=0 m. Find its position vector

(a) In unit-vector notation and as
(b) A magnitude and
(c) An angle relative to the positive direction of the x-axis

• A. $Insufficientdata$
• B. $-5\hat{i}+9\hat{j},\sqrt{106},si{n}^{-1}\left(\frac{-5}{\sqrt{106}}\right)$
• C. $-5\hat{i}+9\hat{k},\sqrt{106},co{s}^{-1}\left(\frac{-5}{\sqrt{106}}\right)$
• D. $-5\hat{i}+9\hat{j},\sqrt{106},co{s}^{-1}\left(\frac{-5}{\sqrt{106}}\right)$

Answer 1

The correct option is D

$-5\hat{i}+9\hat{j},\sqrt{106},co{s}^{-1}\left(\frac{-5}{\sqrt{106}}\right)$

$\left(a\right)\text{It's unit vector notation will be},-5\hat{i}+9\hat{j}+0\hat{k}$
$\left(b\right)Magnitude=\sqrt{(-5{)}^2+(9{)}^2+0^2}$ = $\sqrt{106}$
$\left(c\right)\text{Let the angle with the +ve direction of x-axis be}\alpha$.
$\therefore$ x component = $|\overrightarrow{A}|cos\alpha$
Given $\therefore$ x component is -5
$\therefore -5=\sqrt{106}cos\alpha$
$\Rightarrow cos\alpha =\frac{-5}{\sqrt{106}}$
$\therefore \alpha =co{s}^{-1}\left(\frac{-5}{\sqrt{106}}\right)$