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Find the directional consines of vector `(5hati+2hatj+6hatk)`. Also write the value of sum of squares of directional cosines of this vector. |
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Answer» Let `alpha, beta & lambda` are the angles of vector `(5hati+2hatj+6hatk)` from x,y `&` z-axis respectively. then `cos alpha=(A_(x))/(A)=(6)/(|5hati+2hatj+6hatk|)=(6)/sqrt(65)` `cos gamma=(A_(z))/(A)=(6)/(|55hati+2hatj+6hatk|)=(6)/sqrt(65)` The sum of squares of directional cosines of this vector `cos^(2)alpha+cos ^(2) beta+cos ^(2) gamma=(5^(2)+2^(2)+6^(2))/(65)=(65)/(65)=1` |
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