Position vectors of points A, B, C and D are vec A = 3hat{i} + 4hat{j} + 5hat{k},,vec B = 4hat

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3-1.Vectors

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The position vectors of points $A, B, C$ and $D$ are $\vec A = 3\hat i + 4\hat j + 5\hat k,\,\vec B = 4\hat i + 5\hat j + 6\hat k,\,\vec C = 7\hat i + 9\hat j + 3\hat k$ and $\vec D = 4\hat i + 6\hat j$ then the displacement vectors $\overrightarrow {AB} $ and $\overrightarrow {CD} $ are

A

Perpendicular

B

Parallel

C

Antiparallel

D

Inclined at an angle of $60^o$

Solution

$\overrightarrow{\mathrm{AB}}=\overrightarrow{\mathrm{B}}-\overrightarrow{\mathrm{A}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}$

$\overrightarrow{\mathrm{CD}}=\overrightarrow{\mathrm{D}}-\overrightarrow{\mathrm{A}}=-3 \hat{\mathrm{i}}-3 \hat{j}-3 \hat{\mathrm{k}}$

$\Rightarrow \overrightarrow{\mathrm{CD}}=-\overrightarrow{3 \mathrm{AB}}$

Standard 11

Physics

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