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Chapter 9: Q. 36 (page 630)

Find the vector v in the xy-plane with magnitude 3 if the direction angle of v is 60°.

Short Answer

Expert verified

The vector v in the xy-plane with magnitude 3 and direction angle 60° of v is $\frac{3}{2} i + \frac{3 \sqrt{3}}{2} j$ .

Step by step solution

01

Step 1. Given information

We have been given:

Magnitude $= 3$

and direction angle of v $= 60 °$

We have to find the above vector.

02

Step 2. Find the vector v using formula v=∥v∥(icosθ+jsinθ).

$v = ∥ v ∥ (icos θ + jsin θ) = 3 (icos 60^{\circ} + jsin 60^{\circ}) = 3 (\frac{1}{2} i + \frac{\sqrt{3}}{2} j) = \frac{3}{2} i + \frac{3 \sqrt{3}}{2} j$

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Most popular questions from this chapter

In Problems 39-54,the poplar coordinates of a point are given.Find rectangular coordinates of each point.

$(5, 300 °)$

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