If - -b- - are mutually perpendicular unit vectors- then - - -b- - is equal to

The correct option is A √(3) Since â ,b̂ ,ĉ are mutually perpendicular unit vectors, ⇒| â #160;| =| b̂ #160;| =| ĉ #160;| =1 and #16 ...

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Standard XII

Physics

Distance

If â ,b̂ ,ĉ...

Question

If $^a,^b,^c$ are mutually perpendicular unit vectors, then $∣ ∣^a +^b +^c ∣ ∣$ is equal to

\sqrt{3}

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Solution

The correct option is A $\sqrt{3}$
Since $^a,^b,^c$ are mutually perpendicular unit vectors,
$\Rightarrow |^a | = ∣ ∣^b ∣ ∣ = |^c | = 1$ and $^a .^b =^b .^c =^c .^a = 0$ ...(i)

Now, ${∣ ∣^a +^b +^c ∣ ∣}^{2} = (^a +^b +^c) . (^a +^b +^c)$
$= {|^a |}^{2} + {∣ ∣^b ∣ ∣}^{2} + {|^c |}^{2} + 2 (^a .^b +^b .^c +^c .^a)$
$= 1 + 1 + 1 + 0 = 3$
$\Rightarrow ∣ ∣^a +^b +^c ∣ ∣ = \sqrt{3}$ .

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If ^a,^b,^c are mutually perpendicular unit vectors, then ∣∣^a+^b+^c∣∣ is equal to

The correct option is A √3Since ^a,^b,^c are mutually perpendicular unit vectors,⇒|^a|=∣∣^b∣∣=|^c|=1 and ^a.^b=^b.^c=^c.^a=0 ...(i)Now, ∣∣^a+^b+^c∣∣2=(^a+^b+^c).(^a+^b+^c)=|^a|2+∣∣^b∣∣2+|^c|2+2(^a.^b+^b.^c+^c.^a)=1+1+1+0=3⇒∣∣^a+^b+^c∣∣=√3.

If $^a,^b,^c$ are mutually perpendicular unit vectors, then $∣ ∣^a +^b +^c ∣ ∣$ is equal to