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If vecA =5hati +6hatj+4hatk and vecB =2h...

If `vecA =5hati +6hatj+4hatk and vecB =2hati-2hatj+3hatk`, determine the angle between `vecA and vecB`

Text Solution

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`vecA * vecB =AB cos theta = A_x B_x +A_yB_y + A_zB_z`
`cos theta =(A_x B_x +A_yB_y + A_zB_z)/(AB)`
`cos theta = (A_x B_x +A_yB_y + A_zB_z)/(sqrt(A_x^2 + A_x^2 + A_z^2) sqrt(B_x^2 +B_x^2+B_z^2))`
`cos theta = ((5)(2)+(6)(-2)+(4)(3))/(sqrt(25+36+16)sqrt(4+4+9))`
`=10/(sqrt77.sqrt17)=0.2764`
`theta =cos^(-1) 0.2765 =73^258.`
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