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Question: The (x, y, z) coordinates of two points A and B are given respectively as (0, 4, -2) and (-2, 8, -4)...

The (x, y, z) coordinates of two points A and B are given respectively as (0, 4, -2) and (-2, 8, -4). The displacement vector from A to B is

A

−2i^+4j^−2k^- 2\widehat{i} + 4\widehat{j} - 2\widehat{k}

B

2i^−4j^+2k^2\widehat{i} - 4\widehat{j} + 2\widehat{k}

C

2i^+4j^−2k^2\widehat{i} + 4\widehat{j} - 2\widehat{k}

D

−2i^−4j^−2k^- 2\widehat{i} - 4\widehat{j} - 2\widehat{k}

Answer

−2i^+4j^−2k^- 2\widehat{i} + 4\widehat{j} - 2\widehat{k}

Explanation

Solution

Here, r→A=0i^+4j^−2k^{\overset{\rightarrow}{r}}_{A} = 0\widehat{i} + 4\widehat{j} - 2\widehat{k}

r→B=−2i^+8j^−4k^{\overrightarrow{r}}_{B} = - 2\widehat{i} + 8\widehat{j} - 4\widehat{k}

Displacement vector from A to B is given by

r→=r→B−r→A=(−2i^+8j^−4k^)−(0i^+4j^−2k^)\overset{\rightarrow}{r} = {\overset{\rightarrow}{r}}_{B} - {\overset{\rightarrow}{r}}_{A} = ( - 2\widehat{i} + 8\widehat{j} - 4\widehat{k}) - (0\widehat{i} + 4\widehat{j} - 2\widehat{k})

=−2i^+4j^−2k^= - 2\widehat{i} + 4\widehat{j} - 2\widehat{k}