What is the projection of PQ on F?

Question 86

HardOriginal question

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

What is the projection of $\overrightarrow{PQ}$ on $\vec{F}$ ?

1

Correct answerYour answer

\frac{9 \sqrt{14}}{14}

Correct answerYour answer

3

Correct answerYour answer

9

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Projection of $\overrightarrow{PQ}$ on $\vec{F}$ $= \frac{\vec{F} \cdot \overrightarrow{PQ}}{\lvert \vec{F} \rvert}$ .
$\frac{9}{3} = 3$ .

Worth noting

$\frac{9}{\sqrt{14}}$ divides by $\lvert \overrightarrow{PQ} \rvert$ ; that is the projection of $\vec{F}$ on $\overrightarrow{PQ}$ .

Concept: The projection of one vector on another
Typical timeTypical: 150 s
Your timeYours: —

The rule this testsThe scalar product

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Ten questions from Vectors, at your own pace.

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Ten questions from Vectors, at your own pace.

What is the projection of PQ on F?

Question 86

Explanation