Vector Equation

Hi,

If anyone can help me with the following question I would be eternally grateful.

"Write down a vector d which is parallel to the line r=(-1, -6, 1) + t(1, 2, 1).

The point P lies on the above line. Find the value of t for which

\overrightarrow {O P}

.d = 0, where O is the origin. Hence determine the coordinates of P."

I have found a parallel vector of d=(1, 2, 1) (I hope this is correct anyway!).

But now I am stuck. Any direction or hints appreciated.

Do you understand how to evaluate the scalar product?

\begin{pmatrix} a \\ c \\ e \end{pmatrix} \bullet \begin{pmatrix} b \\ d \\ f \end{pmatrix} = ab + cd + ef

Reply 3

ExWunderkind

OP

12

Original post by Mr M

\begin{pmatrix} a \\ c \\ e \end{pmatrix} \bullet \begin{pmatrix} b \\ d \\ f \end{pmatrix} = ab + cd + ef

Ah ok, so what you are saying is I find the dot product of

r=(1, -6, 1) and d=(1, 2, 1)

and take it from there?

Original post by ExWunderkind

Ah ok, so what you are saying is I find the dot product of

r=(1, -6, 1) and d=(1, 2, 1)

and take it from there?

Part of r seems to be missing?

Reply 5

ExWunderkind

OP

12

Original post by Mr M

Part of r seems to be missing?

Yes, but can I not set t=0?

Original post by ExWunderkind

Yes, but can I not set t=0?

Why would you think you could do that? That will take you to a point on the line but it isn't point P. You need to form a linear equation in t.

Reply 7

ExWunderkind

OP

12

Original post by Mr M

Why would you think you could do that? That will take you to a point on the line but it isn't point P. You need to form a linear equation in t.

Thank you Mr M by the way, I appreciate this.

I think I have it set now. Using my vector d and the line segment OP I derived three linear equations and added them together to give me t = 2.

Which I can slot back into my original equation for the line and find P. Is that correct?

Original post by ExWunderkind

Thank you Mr M by the way, I appreciate this.

I think I have it set now. Using my vector d and the line segment OP I derived three linear equations and added them together to give me t = 2.

Which I can slot back into my original equation for the line and find P. Is that correct?