What are the components of the vector between the origin and the polar coordinate $(16, \frac{7 π}{6})$ $(16, (7pi)/6)$ ?

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What are the components of the vector between the origin and the polar coordinate $(16, \frac{7 π}{6})$ $(16, (7pi)/6)$ ?

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Answer 1 · 2016-12-30T13:14:10

$(- 8 \sqrt{3}, - 8)$ $(-8sqrt3,-8)$ or $- 8 \sqrt{3} ˆ i - 8 ˆ j$ $-8sqrt3hati-8hatj$ ,

Explanation:

Components of a vector between the origin and the polar coordinate $(r, θ)$ $(r,theta)$ are $(x cos θ, y sin θ)$ $(xcostheta,ysintheta)$ .
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Here we have $r = 16$ $r=16$ and $θ = \frac{7 π}{6}$ $theta=(7pi)/6$

Hence components are $(16 cos (\frac{7 π}{6}), 16 sin (\frac{7 π}{6}))$ $(16cos((7pi)/6), 16sin((7pi)/6))$

or $(16 \times (- \frac{\sqrt{3}}{2}), 16 \times (- \frac{1}{2}))$ $(16xx(-sqrt3/2),16xx(-1/2))$

or $(- 8 \sqrt{3}, - 8)$ $(-8sqrt3,-8)$

We can also write it as $- 8 \sqrt{3} ˆ i - 8 ˆ j$ $-8sqrt3hati-8hatj$ ,

where $ˆ i$ $hati$ and $ˆ j$ $hatj$ are unit vectors along $x$ $x$ -axis and $y$ $y$ -axis respectively.

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What are the components of the vector between the origin and the polar coordinate $(16, \frac{7 π}{6})$ $(16, (7pi)/6)$ ?

1 Answer

Explanation:

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What are the components of the vector between the origin and the polar coordinate (16,7π6)(16, (7pi)/6)?

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What are the components of the vector between the origin and the polar coordinate $(16, \frac{7 π}{6})$ $(16, (7pi)/6)$ ?