If a - b - c are three mutually perpendicular unit vectors- then - a - b - c - is equal toA- 3B- -3C- -2D- 2

The correct option is B √(3)Given that a, b, c are mutually perpendicular, so, nbsp; a . b = nbsp;b . c = nbsp; c . a = 0 and a, b and c are unit vectors ...

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Byju's Answer

Standard XII

Physics

Vector Addition

If a , b , c ...

Question

If $\to a, \to b, \to c$ are three mutually perpendicular unit vectors, then $| \to a + \to b + \to c |$ is equal to

3

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\sqrt{3}

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\sqrt{2}

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2

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Solution

The correct option is B $\sqrt{3}$
Given that $\to a, \to b, \to c$ are mutually perpendicular, so,
$\to a . \to b = \to b . \to c = \to c . \to a = 0$
and $\to a, \to b$ and $\to c$ are unit vectors, so
$| \to a | = | \to b | = | \to c | = 1$
Now, $\to c$ are unit vectors, so
$| \to a + \to b + \to c |^{2} = | \to a |^{2} + | \to b |^{2} + | \to c |^{2} + 2 \to a . \to b + 2 \to b . \to c + 2 \to c . \to a$
$\Rightarrow | \to a + \to b + \to c |^{2} = 3$
$∴ | \to a + \to b + \to c | = \sqrt{3}$

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