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MATH / In a 3-dimensional coordinate system with x-, y-, and z-axes, P is a point on the line y=−x+1 in the xy-plane and Q is a point on the line z=−2x+1 in the xz-plane. Compute the smal…

Problem

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problem

In a 3-dimensional coordinate system with xx-, yy-, and zz-axes, PP is a point on the line y=−x+1y = -x + 1 in the xyxy-plane and QQ is a point on the line z=−2x+1z = -2x + 1 in the xzxz-plane. Compute the smallest possible value for PQ.PQ.
Plain-text mathematical notation (without MathML)
In a 3-dimensional coordinate system with x-, y-, and z-axes, P is a point on the line y=−x+1 in the xy-plane and Q is a point on the line z=−2x+1 in the xz-plane.  Compute the smallest possible value for PQ.
Original LaTeX notation
In a 3-dimensional coordinate system with $x$-, $y$-, and $z$-axes, $P$ is a point on the line $y = -x + 1$ in the $xy$-plane and $Q$ is a point on the line $z = -2x + 1$ in the $xz$-plane.  Compute the smallest possible value for $PQ.$

level

Level 5

type

Precalculus

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Source and history

task_id
e460e825-e790-58ea-afb4-8c3fe3f784ac
task_key
precalculus--test--e460e825-e790-58ea-afb4-8c3fe3f784ac
task_revision_id
1
config / split
precalculus / test

Official source

initial import