Step by step please Let u = (4. - 4, - 3) and v = (4.2.1). Find a unit vector w

Question

Step by step please

Let u = (4. - 4, - 3) and v = (4.2.1). Find a unit vector w which is orthogonal(perpendicular) to both u and v. (For the vector (1.2.3) type .) w =

Explanation / Answer

If (x, y, z) is one of such vectors, then its dot product by a and b is 0. So, = 0 and = 0. Hence 4x -4y -3z = 0 4x + 2y + z = 0 If we subtract these 2 equations, we get -6y-4z=0 => 3y+2z=0=>y=-2z/3 4x - 4z/3 + z =0 =>4x-z/3=0 =>x=z/12 It follows the vectors perpendicular to v and u are of the form v = (z/12, -2z/3, z), u ? R and ||v|| = v1.4514 |z| = 1.205 |z| It follows the only unit vector perpendicular to a and b corresponds to z = 1/2.05 = 0.83, so the vector (0.83/12,-2*0.83/3 , 0.83) = (0.07, -0.553, 0.83)

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