Question

Determine whether the vectors u and v are parallel, orthogonal, or neither.

u = <9, 3>, v = <36, 12>

Answer 1

Answer: Vectors u and v are parallel.

Explanation:

Since we have given that

u=<9,3>

and v=<36,12>

First we write it as in parallel condition:

`u=kv\\\\<9,3>=k<36,12>\\\\<9,3>=<36k,12k>\\\\\text{ Comparing term wise term}\\\\9=36k\\\\k=(9)/(36)\\\\k=(1)/(4)\\\\Similarly,\\\\3=12k\\\\k=(3)/(12)=(1)/(4)`

Since both have same constant of proportionality i.e.'k'.

So, it is parallel.

And if it is parallel, then, it can't be perpendicular.

Hence, vectors u and v are parallel.

Answer 2

Vectors u = (9,3) and v = (36,12) are parallel. Because vector “v” is a multiple of vector “u”.

The two vectors can also be written as;

(9,3) = 4 x (9,3)

Hence there is only the addition of a scalar quantity “4”.