Question

is the vector <1,-3,2> orthogonal (forms a 90 degree angle) with the line given by the following parametric equations: x=1+t, y=-2+2t,z=5

Answer 1

How can you find if two things are orthogonal?
Pro tip: Its a type of product.

Answer 2

the vector of the line is the "t" coeffs.

<1,2,5>; now dot it to the suspected vector and see if we get the 0

Answer 3

ack ... that 5 got me lol

there is no t in z

Answer 4

<1,2,0>

Answer 5

i get 1-6 ... so no zero

Answer 6

Ah ok, thanks mate

Answer 7

You have a vector
\[\vec{a}=\left \langle 1,-3,2 \right \rangle\]And the parametric equations
\[x=1+t\]\[y=-2+2t\]\[z=5\]These equations can be de-parametrized as
\[\vec{r}(t)=(1,-2,5)+t\left \langle 1,2,0 \right \rangle\]Let's set
\[\vec{b}=\left \langle 1,2,0 \right \rangle\]Now,
\[\vec{a}\cdot\vec{b}=\left \langle 1,-3,2 \right \rangle \cdot\left \langle 1,2,0 \right \rangle=1-6+0=-5\]Therefore, they're not orthogonal.