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Vector Algebra question

2023 · 29 Jan · Shift 2 · Q33

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JEE Main
Mathematics
Vector Algebra
2023 · 29 Jan · Shift 2 · Q33

Vector Algebra question

2023 · 29 Jan · Shift 2 · Q33

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let

\overrightarrow a = 4\widehat i + 3\widehat j

and

\overrightarrow b = 3\widehat i - 4\widehat j + 5\widehat k

. If

\overrightarrow c

is a vector such that

\overrightarrow c .\left( {\overrightarrow a \times \overrightarrow b } \right) + 25 = 0,\overrightarrow c \,.(\widehat i + \widehat j + \widehat k) = 4

, and projection of

\overrightarrow c

on

\overrightarrow a

is 1, then the projection of

\overrightarrow c

on

\overrightarrow b

equals :

A
$\frac{3}{\sqrt2}$
B
$\frac{1}{\sqrt2}$
C
$\frac{1}{5}$
D
$\frac{5}{\sqrt2}$

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