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Vectors · Question 77 of 125

What is the cosine of the angle between F and PQ?

Question 77

MediumOriginal question

A constant force F⃗=2i^+2j^+k^\vec{F} = 2\hat{i} + 2\hat{j} + \hat{k} moves a particle from P(1,−1,2)P(1, -1, 2) to Q(3,2,1)Q(3, 2, 1). The work done is F⃗⋅PQ→\vec{F} \cdot \overrightarrow{PQ}.

What is the cosine of the angle between F⃗\vec{F} and PQ→\overrightarrow{PQ}?

Options for question 77

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. ∣F⃗∣=3\lvert \vec{F} \rvert = 3 and ∣PQ→∣=14\lvert \overrightarrow{PQ} \rvert = \sqrt{14}.

  2. cos⁡θ=9314=314\cos \theta = \frac{9}{3\sqrt{14}} = \frac{3}{\sqrt{14}}.

Worth noting

914\frac{9}{14} divides by ∣PQ→∣2\lvert \overrightarrow{PQ} \rvert^{2} instead of ∣F⃗∣∣PQ→∣\lvert \vec{F} \rvert \lvert \overrightarrow{PQ} \rvert.

Concept
The angle between two vectors
Typical time
120 s
Your time
—
The rule this testsThe scalar product
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