If A = 2 i + 3 j - k and B = - i + 3 j + 4 k then projection of A… - Vidyadip

MCQ

If $\overrightarrow {\rm A} = 2\hat i + 3\hat j - \hat k$ and $\overrightarrow B = - \hat i + 3\hat j + 4\hat k$ then projection of $\overrightarrow A $ on $\overrightarrow B $ will be

A
$\frac{3}{{\sqrt {13} }}$
✓
$\frac{3}{{\sqrt {26} }}$
C
$\sqrt {\frac{3}{{26}}} $
D
$\sqrt {\frac{3}{{13}}} $

✓

Answer

Correct option: B.

$\frac{3}{{\sqrt {26} }}$

b
(b) $|\overrightarrow {\rm A} |\, = \,\sqrt {{2^2} + {3^2} + {{( - 1)}^2}} $$ = \sqrt {4 + 9 + 1} $ $ = \sqrt {14} $

$|\overrightarrow B |\, = \,\sqrt {{{( - 1)}^2} + {3^2} + {4^2}} $ $ = \sqrt {1 + 9 + 16} $ $ = \sqrt {26} $

$\overrightarrow A \,.\,\overrightarrow B = \,2\,( - 1) + 3 \times 3 + ( - 1)\,(4) = 3$

The projection of $\overrightarrow A \,\,{\rm{on}}\,\overrightarrow B $ $ = \frac{{\overrightarrow A \,.\,\overrightarrow B }}{{|\overrightarrow B |}}$ $ = \frac{3}{{\sqrt {26} }}$

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