InterviewSolution
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InterviewSolution
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Vector ` vec O A= hat i+2 hat j+2 hat k`turns through a right anglepassing through the positive x-axis on the way. Show that the vector in its new position is`(4 hat i- hat j- hat k)/(sqrt(2))dot` |
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Answer» Let the new vector be `vec(OB)= xhati+yhatj=zhatk` According to the given condition, we have `|vec(OB)|=|vec(OA)|=3 Rightarrowx^(2)+y^(2)+z^(2)=9` `vec(OA)vec(OB)Rightarrowx+2y+2z=0` Since with turing `vec(OA)`, it passes through the postivie x-axis on the way, vectors `vec(OA),vec(OB)and lambdahati` coplanar . thus, `|{:(x,y,z),(1,2,2),(lambda,0,0):}|=0` or y-z=0 solving (i) (ii) and (iii) for x,y and z. we have x-4y=-4z `Rightarrow 16y^(2)+y^(2)+y^(2)=9` `Rightarrowy=+-1/sqrt2` `Rightarrow vec(OB) = +-(4/sqrt2hati-1/sqrt2hatj-1/sqrt2hatk)` since angle between `vec(OB) and hati` is acute, `vec(OB)=4/sqrt2hati-1/sqrt2hatj-1/sqrt2hatk` |
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