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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:


A
π4
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B
π3
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C
π2
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D
3π4
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Solution

The correct option is B π3
2ac=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 cosθ=(0)(1)+(1)(0)+(1)(1)1+11+1=12θ=π3

Mathematics

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