Homework SourseI need to know what values for a are the vectors x and y col
I need to know what values for a are the vectors x and y collinear.
Vector x = (3,a,9)
Vector y = (a,12,18)
I want this solved using the dot product law or rule thing where x dot y = |x||y|costheta
Vector x = (3,a,9)
Vector y = (a,12,18)
I want this solved using the dot product law or rule thing where x dot y = |x||y|costheta
Solution
If two vectors x and y are colinear then x.y = |x||y| ...(i)
because cos is 1.
here x.y = 3xa + ax 12+9x18 = 15a +162
|x|= (a2 + 90)
|y| = (a2+468)
on applying equation i
(a2 + 90)(a2+468) = (15a +162)2
=> a4 + 558a2 + 42120 = 225a2 + 4860a +26244
=> a4 + 333a2 -4860a + 15876 = 0
which has a solution a =6
therefore a = 6 will make x and y colinear.
