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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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