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Question

Find the angle between the vectors (2^i+^j+3^k) and (3^i2^j+^k).

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Solution

Let a=2^i+^j+3^k,b=3^i2^j+^k

We know that ab=|a||b|cosθ, where θ is the angle between a and b.

ab=(2^i+^j+3^k)(3^i2^j+^k)

=62+3

ab=7

|a|=22+12+32=4+1+9=14

|b|=32+(2)2+12=9+4+1=14

Substitute the values in ab=|a||b|cosθ we get

7=1414cosθ

7=14cosθ

cosθ=714

cosθ=12

θ=cos1(12)

θ=π3

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