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

2 Answers
Aug 9, 2018

x = -8

Explanation:

Recall..

For x to be parallel it means the gradients must be equal to 1

m = 1

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

y_2 = -6

y_1 = x

x_2 = 4

x_1 = 2

Plugging in the values..

m_1 = ((-6) - x)/(4 - 2) = (-6 - x)/2

Therefore;

(-6 - x)/2 = 1

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

Cross multiply;

(-6 - x) xx 1 = 1 xx 2

-6 - x = 2

-x = 2 + 6

-x = 8

x = -8

Aug 9, 2018

x=-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.