If a-2k- b - 2-k- then c-2-3k- then the angle between 2a-c and a-b is-

2 a c=2( î+ĵ+2k̂) ( 2î+ĵ+3k̂)=ĵ+k̂ a+b=( î+ĵ+2k̂)+(2î ĵ k̂)=î+k̂ If θ is the angle between 2a c, a+b then cos θ =(0)(1)+(1)(0)+(1)(1)/√(1+1)√(1+1)=1/2⇒θ =π/3 ...

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Standard XIII

Mathematics

Angle between Two Vectors

If a=-î+ĵ+2k̂...

Question

If $a = -^i +^j + 2^k$ , $b = 2^i -^j -^k$ then $c = - 2^i +^j + 3^k$ , then the angle between 2a-c and a+b is:

\frac{π}{4}

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\frac{π}{3}

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\frac{π}{2}

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\frac{3 π}{4}

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Solution

The correct option is B $\frac{π}{3}$
$2 a - c = 2 (-^i +^j + 2^k) - (- 2^i +^j + 3^k) =^j +^k$
$a + b = (-^i +^j + 2^k) + (2^i -^j -^k) =^i +^k$
If $θ$ is the angle between 2a-c, a+b then $c o s θ = \frac{(0) (1) + (1) (0) + (1) (1)}{\sqrt{1 + 1} \sqrt{1 + 1}} = \frac{1}{2} \Rightarrow θ = \frac{π}{3}$

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If a=−^i+^j+2^k, b=2^i−^j−^k then c=−2^i+^j+3^k, then the angle between 2a-c and a+b is:

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