v = −i+2j+k, w = −3i+6j+3k Find the angle θ between the vectors v and w

v = −i+2j+k, w = −3i+6j+3k Find the angle θ between the vectors v and w
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||v||=√(1+4+1)=√6; ||w||=√(9+36+9)=√54. ||v||*||w||=√324=18.

v•w=(-1)(-3)+2*6+1*3=3+12+3=18.

cos(theta)=v•w/||v||*||w||=18/18=1 so theta=0 (vectors are parallel).
by Top Rated User (1.1m points)

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