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Question: The magnitude of a given vector with end points (4, – 4, 0) and (– 2, – 2, 0) must be...

The magnitude of a given vector with end points (4, – 4, 0) and (– 2, – 2, 0) must be

A

6

B

525\sqrt{2}

C

4

D

2102\sqrt{10}

Answer

2102\sqrt{10}

Explanation

Solution

r→=r→2−r→1=(−2i^−2j^+0k^)−(4i^−4j^+0k^)\overrightarrow{r} = {\overrightarrow{r}}_{2} - {\overrightarrow{r}}_{1} = ( - 2\widehat{i} - 2\widehat{j} + 0\widehat{k}) - (4\widehat{i} - 4\widehat{j} + 0\widehat{k})

⇒ r→=−6i^+2j^+0k^\overrightarrow{r} = - 6\widehat{i} + 2\widehat{j} + 0\widehat{k}

∴ ∣r→∣=(−6)2+(2)2+02=36+4=40=210|\overrightarrow{r}| = \sqrt{( - 6)^{2} + (2)^{2} + 0^{2}} = \sqrt{36 + 4} = \sqrt{40} = 2\sqrt{10}