How do you write the vector equation that passes through point (-6,10) and parallel to <3,2>?

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Answer 1 · 2016-08-26T11:38:09

$r = < x, y > = < 3 t - 6, 2 t + 10 >$ $r = < x, y > =<3t-6, 2t+10>$

If a vector $V$ $V$ is parallel to the vector $U$ $U$ , then $V = t U$ $V=t U$ , where t is

a scalar.l

Let $r = < x, y >$ $r = < x, y >$ be the position vector $O P$ $OP$ to the point P(x, y) on

the line through A(-6, 10) in the direction of $< 3, 2 >$ $<3, 2>$ . Then,

Vector $A P$ $AP$

$= O P - O A$ $= OP - OA$

$= < x + 6, y - 10 >$ $= < x+6, y-10 >$

$= t < 3, 2 >$ $= t <3, 2 >$ , .

So, $r = < x, y > = < 3 t - 6, 2 t + 10 >$ $r = < x, y > = < 3t-6, 2t+10 >$