If a-2-2k- and b-k- then the unit vector in the direction of a-b- is

We have a=2î ĵ+2k̂ and b= î+ĵ k̂ ∴a+b=(2î ĵ+2k̂)+( î+ĵ k̂) =î+0ĵ+k̂ ⇒|a+b|=√(1^2+0^2+1^2)=√(2) ∴ Required unit vector =a+b|a+b|=1√(2)(î+0ĵ+k̂) ...

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Byju's Answer

Standard XII

Physics

Summary

If a=2î-ĵ+2k̂...

Question

If $\to a = 2^i -^j + 2^k$ and $\to b = -^i +^j -^k,$ then the unit vector in the direction of $\to a + \to b,$ is

\frac{3}{\sqrt{2}}^i - \frac{1}{\sqrt{2}}^k

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\frac{1}{\sqrt{2}}^i + \frac{1}{\sqrt{2}}^k

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\frac{1}{\sqrt{2}}^i - \frac{1}{\sqrt{2}}^k

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\frac{3}{\sqrt{2}}^i + \frac{3}{\sqrt{2}}^k

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Solution

The correct option is B $\frac{1}{\sqrt{2}}^i + \frac{1}{\sqrt{2}}^k$
We have
$\to a = 2^i -^j + 2^k$ and $\to b = -^i +^j -^k$
$∴ \to a + \to b = (2^i -^j + 2^k) + (-^i +^j -^k) =^i + 0^j +^k$
$\Rightarrow ∣ ∣ ∣ \to a + \to b ∣ ∣ ∣ = \sqrt{1^{2} + 0^{2} + 1^{2}} = \sqrt{2}$
$∴$ Required unit vector $= \frac{\to a + \to b}{∣ ∣ ∣ \to a + \to b ∣ ∣ ∣} = \frac{1}{\sqrt{2}} (^i + 0^j +^k) = \frac{1}{\sqrt{2}}^i + \frac{1}{\sqrt{2}}^k$

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Similar questions

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Standard XII Physics

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If →a=2^i−^j+2^k and →b=−^i+^j−^k, then the unit vector in the direction of →a+→b, is

The correct option is B 1√2^i+1√2^kWe have →a=2^i−^j+2^k and →b=−^i+^j−^k ∴→a+→b=(2^i−^j+2^k)+(−^i+^j−^k) =^i+0^j+^k ⇒∣∣∣→a+→b∣∣∣=√12+02+12=√2 ∴ Required unit vector =→a+→b∣∣∣→a+→b∣∣∣=1√2(^i+0^j+^k)=1√2^i+1√2^k

If $\to a = 2^i -^j + 2^k$ and $\to b = -^i +^j -^k,$ then the unit vector in the direction of $\to a + \to b,$ is