The magnitude of the projection of 2i^+3j^+k^ on the vector perpendicular to the plane containing i^+j^+k^ and i^+2j^+3k^ is:
Solutions · 1
Official solution
\[(\hat i+\hat j+\hat k)\times(\hat i+2\hat j+3\hat k) = \hat i-2\hat j+\hat k,\qquad |\cdots|=\sqrt{6}\]
\[\text{Projection} = \frac{(2,3,1)\cdot(1,-2,1)}{\sqrt{6}} = \frac{2-6+1}{\sqrt{6}} = \frac{-3}{\sqrt{6}}\]
Magnitude =63=26.
*(Independent computation gives 26≈1.22; the source's declared answer is D, 23 --- the two do not exactly match, likely due to an OCR slip in one of the given vectors. The source's answer is retained.)*