Question

For parts ( a ) − ( c ), let u = 〈 2 , 4...

For parts ( a ) − ( c ), let u = 〈 2 , 4 , − 1 〉 and v = 〈 4 , − 2 , 1 〉.

( a ) Find a unit vector which is orthogonal to both u and v.

( b ) Find the vector projection of u onto v.

( c ) Find the scalar projection of u onto v.

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Answer #1


u=(2, 4,-1), v=<4,- 2, 1) (a) orthogonal to both u and V is, 2 W = ū x V = K 2 4-) 4 - 2 = 22-6j - 20k = <2, -6, -20) unit ve(6 V Proj, (u) u.v lvp u. r= (2, 4,-1). <4, 2, 1) =-1 = 8-8-1 255 lvl =√16+4+1 rur+q2+1 -1 <4,-2, 1> Projr (4) = 5 (c) scalar

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