First slide

Planes in 3D

Question

P = (0, 1, 0), Q = (0, 0, 1) then projection of $\vec{P Q}$ on the plane x + y + z = 3 is

Difficult

A

$\sqrt{2}$
B

$- \sqrt{2}$
C

$2 \sqrt{2}$
D

$3 \sqrt{2}$

Solution

P (0, 1, 0) Q(0, 0, 1)
$x + y + z - 3 = 0$

Dr’s PQ are (0,1-1)

$\frac{x}{3} + \frac{y}{3} + \frac{z}{3} = 1$

Dr’s of line (1, 1, 1)

$P Q \sin θ = \sqrt{1 + 1} = \sqrt{2}$

$θ = 90$

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