Find the sine of the angle between the vectors

Asked by admin @ in Math viewed by 284 People

Find the sine of the angle between the vectors a=3i-4j+5k and b=i-j+k

Answered by admin @


The sine of angle between the vectors is √6/12.

  • We have to find the sine of angle between the following vectors, a=3i-4j+5k and b=i-j+k
  • The sine of the angle between vectors is given by

sinθ = \frac{|\bar a \times \bar b|}{\bar a . \bar b}

  • We first find the value of,

\bar a \times \bar b = \left[\begin{array}{ccc}i&j&k\\3&-4&5\\1&-1&1\end{array}\right] = i(-4+5)-j(3-5)+k(-3+4)= i-2j+k

  • Now, |\bar a \times \bar b| = | i-2j+k| = \sqrt{1^2+(-2)^2+1^2} = \sqrt{1+4+1} = \sqrt{6}
  • Now, \bar a . \bar b[\tex] = (3i-4j+5k)(i-j+k) = 3+4+5 = 12Now , sinθ = [tex]\frac{\sqrt{6}}{12}

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