Find the x that makes <2,x> and <4,-6> parallel?

2 Answers
Aug 9, 2018

x = -8x=8

Explanation:

Recall..

For xx to be parallel it means the gradients must be equal to 11

m = 1m=1

m_1 = (y_2 - y_1)/(x_2 - x_1)m1=y2y1x2x1

y_2 = -6y2=6

y_1 = xy1=x

x_2 = 4x2=4

x_1 = 2x1=2

Plugging in the values..

m_1 = ((-6) - x)/(4 - 2) = (-6 - x)/2m1=(6)x42=6x2

Therefore;

(-6 - x)/2 = 16x2=1

(-6 - x)/2 = 1/16x2=11

Cross multiply;

(-6 - x) xx 1 = 1 xx 2(6x)×1=1×2

-6 - x = 26x=2

-x = 2 + 6x=2+6

-x = 8x=8

x = -8x=8

Aug 9, 2018

x=-3x=3.

Explanation:

By definition, two non-null vectors

vecu, &, vecv" are parallel "iff vecu=kvecv" for some "k in RR-{0}.

:. (2,x)=k(4,-6) rArr 4k=2, -6k=x.

:. k=2/4=1/2.

:. x=-6k=-6*1/2=-3.