The direction cosines of the vector 3i - 4j + 5k are - Vidyadip

MCQ

The direction cosines of the vector $3i - 4j + 5k$ are

A
$\frac{3}{5},\,\frac{{ - 4}}{5},\frac{1}{5}$
✓
$\frac{3}{{5\sqrt 2 }},\,\frac{{ - 4}}{{5\sqrt 2 }},\frac{1}{{\sqrt 2 }}$
C
$\frac{3}{{\sqrt 2 }},\,\frac{{ - 4}}{{\sqrt 2 }},\,\frac{1}{{\sqrt 2 }}$
D
$\frac{3}{{5\sqrt 2 }},\,\,\frac{4}{{5\sqrt 2 }},\,\frac{1}{{\sqrt 2 }}$

✓

Answer

Correct option: B.

$\frac{3}{{5\sqrt 2 }},\,\frac{{ - 4}}{{5\sqrt 2 }},\frac{1}{{\sqrt 2 }}$

b
(b) Vector$\overrightarrow A = 3i - 4j + 5k$ We know that direction cosines of $\overrightarrow A $

$ = \frac{3}{{\sqrt {{3^2} + {4^2} + {5^2}} }},\,\frac{{ - 4}}{{\sqrt {{3^2} + {4^2} + {5^2}} }},\,\frac{5}{{\sqrt {{3^2} + {4^2} + {5^2}} }}$

$ = \frac{3}{{5\sqrt 2 }},\,\frac{{ - 4}}{{5\sqrt 2 }},\,\frac{1}{{\sqrt 2 }}$.

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