How do you write the vector equation that passes through point (1,0) and parallel to <-2,-4>?

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Answer 1 · 2016-12-08T09:48:07

$\to r = (λ + 1) \to i - 2 \to j$ $vecr=(lambda+1)veci-2vecj$

the vector eqn. of a line is given by

$\to r = \to a + λ \to d$ $vecr=veca+lambdavecd$

where

$\to r$ $vecr" "$ is the general vector point on the line

$\to a$ $veca" "$ is a known vector point on the line

$\to d$ $vecd" "$ is the direction of the line

$λ$ $lamda" "$ is a scalar

in this case $\to a = \to i$ $veca=veci$

$\to d = 2 \to i - 4 \to j$ $vecd=2veci-4vecj$ or $\to i - 2 \to j$ $veci-2vecj" "$ in its simplest form

$:.vecr=veci+lambda(veci-2vecj)=(lambda+1)veci-2vecj$