What is the unit vector that is orthogonal to the plane containing (8i + 12j + 14k) and (3i – 4j + 4k) ?

1 Answer
Yonas Yohannes
Jan 20, 2016

Use the cross product to find the vector v_1 xx v_2_|_ = v_3
v_3 =104i +10j -68k
vec(u_3) = 1/sqrt(104^2+10^2+68^2)(104i +10j -68k)

Explanation:

let vec(v_1) = (8, 12, 14) and vec(v_2) = (3, -4, 4)
cross product vec(v_1)xx vec(v_2) = [(12xx4) +(14xx4)] i + [(14xx3) -(8xx4)] j + [(8xx-4 - 12xx3)]k

Simplify to get the Orthogonal vector.

vec(v_3) =104i +10j -68k
To calculate the unit vector find:
vec(u_3) = 1/|vec(v_3)| vec(v_3)
where: |vec(v_3)| = magnitude
|vec(v_3)| = sqrt(104^2+10^2+68^2)

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