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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

Insufficient data

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B

5^i+9^j, 106, sin1(5106)

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C

5^i+9^k, 106, cos1(5106)

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D

5^i+9^j, 106, cos1(5106)

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Solution

The correct option is D −5^i+9^j, √106, cos−1(−5√106) (a) It's unit vector notation will be,−5^i+9^j+0^k (b)Magnitude=√(−5)2+(9)2+02 = √106 (c) Let the angle with the +ve direction of x-axis be α. ∴ x component = |→A| cosα Given ∴ x component is -5 ∴−5=√106 cosα ⇒cos α=−5√106 ∴α=cos−1(−5√106)

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