Question

if unit vector i cap is rotated through an angle of 30 degree clockwise, then new vector obtained is


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Answer 1

Answer:

$(4) \frac{\sqrt{3}i}{2}-\frac{j}{2}$

Explanation:

1) We have a unit vector "i" cap which  is rotated by an angle of 30 degree clockwise.

Then,required figure is shown.

2) X- component of new vector:

$x=cos(30^{\circ})i=\frac{\sqrt{3}}{2}i$

3)  Y- component of new vector:

Since, y component is in downward  direction ,so we add negative sign to it.

$y=-sin(30^{\circ})=-\frac{1}{2}j$

Hence, required vector is

$\vec{r}=\frac{\sqrt{3}}{2}i-\frac{1}{2}j$