Let $\ell$ be the line parametrized as $(t, 2t+1, 3t+2)$ and let $P$ be the plane with equation $x+y+z = 1$.
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2026-04-01 04:39:45.1775018385
Let $\ell$ be the line parametrized as $(t, 2t+1, 3t+2)$ and let $P$ be the plane with equation $x+y+z = 1$.
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What to do for (a): multiply the matrix $A$ by $\pmatrix{t\\2t+1\\3t+2}$
and show that the resulting point is in the plane
(which is characterized by sum of components equal $1$).
What to do for (b): multiply the matrix $B$ by $\pmatrix{ x\\y\\1-x-y}$
and show that the resulting point $\pmatrix{X\\Y\\Z}$is on the line
(which is characterized by $X=\dfrac{Y-1}2=\dfrac{Z-2}3$).