What is the unit vector that is orthogonal to the plane containing $(8i + 12j + 14k)$ and $(2i+j+2k)$ ?

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Answer 1 · 2016-08-06T10:30:40

Two steps are required:

The unit vector, then, is given by:

$(10/sqrt500i+12/sqrt500j-16/sqrt500k)$

$(8i+12j+14k) xx (2i+j+2k)$
$=((12*2-14*1)i + (14*2-8*2)j + (8*1-12*2)k)$
$=(10i+12j-16k)$

To normalise a vector, find its length and divide each coefficient by that length.

$r=sqrt(10^2+12^2+(-16)^2)=sqrt500~~22.4$

The unit vector, then, is given by:

$(10/sqrt500i+12/sqrt500j-16/sqrt500k)$

What is the unit vector that is orthogonal to the plane containing (8i + 12j + 14k) (8i + 12j + 14k) and (2i+j+2k) (2i+j+2k) ?