What is the unit vector that is orthogonal to the plane containing # (-2i- 3j + 2k) # and # (3i – 4j + 4k) #?

1 Answer
Jan 20, 2016

Answer:

Take the cross product of the 2 vectors
#v_1 = (-2, -3, 2) and v_2 = (3, -4, 4) #
Compute #v_3 = v_1 xx v_2 #
#1/sqrt(501) (-4, 14, 17)#

Explanation:

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The #v_3 = (-4, 14, 17)#
The magnitude of this new vector is:
#|v_3| = 4^2 + 14^2 + 17^2#
Now to find the unit vector normalize our new vector
#u_3 = v_3/ (sqrt( 4^2 + 14^2 + 17^2)); = 1/sqrt(501) (-4, 14, 17)#