First slide

Straight lines in 3D

Question

The line of intersection of the planes $x + y + z - 1 = 0, 4 x + y - 2 z + 2 = 0$ passes through the point

Very Easy

A

$(1, 0, 1)$
B

$(2, 0, 1)$
C

$(0, 0, 1)$
D

$(1, 0, 0)$

Solution

The equations of the given plane are $x + y + z - 1 = 0, 4 x + y - 2 z + 2 = 0$
Substitute $y = 0$ in the above equations and then solve for the other two variables.
Hence, $x = 0, z = 1$
One of the points on the line of intersection of two planes is $(0, 0, 1)$

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