If a - b - c are three mutually perpendicular unit vectors- then - a - b - c - is equal toA- 3B- 1C- -3D- 1-2

The correct option is A 3 nbsp;a,b,c are mutually perpendicular unit vectors. ⇒ |a|= |b|= |c|=1 & a·b=b·c=c·a=0 Consider |a+b+c|^2 = nbsp;(a+b+c)·(a+b+ ...

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Standard XII

Physics

Relative Velocity

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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\frac{1}{\sqrt{2}}

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Solution

The correct option is A $3$
$\to a, \to b, \to c$ are mutually perpendicular unit vectors.
$\Rightarrow | \to a | = | \to b | = | \to c | = 1$
$& \to a \cdot \to b = \to b \cdot \to c = \to c \cdot \to a = 0$
$Consider | \to a + \to b + \to c |^{2}$
$= (\to a + \to b + \to c) \cdot (\to a + \to b + \to c)$
$= | \to a |^{2} + | \to b |^{2} + | \to c |^{2} + 2 (\to a \cdot \to b + \to b \cdot \to c + \to c \cdot \to a)$
$= 1^{2} + 1^{2} + 1^{2} = 3$
$∴ | \to a + \to b + \to c | = \sqrt{3}$

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

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