Finding the line that perpendiculary intersects a vector.

[H.Bisho18]

Hi

So i have a vector equation

L1: r = 8i + 12j + 14k + t(i + j - k)

Given that the line OP is perpendicular to L1 and P lies on L1 and O is the origin find P
I can't remember how to do it ( summers fried my brain)
I've dotted ( i + j + k) with ( a + b +c ) and set it equal to 0 ending up with
a + b - c = 0 but i can't see a step on from there

Is this the way to go about it?

 

[pka]

So i have a vector equation
L1: r = 8i + 12j + 14k + t(i + j - k)
Given that the line OP is perpendicular to L1 and P lies on L1 and O is the origin find P
I can't remember how to do it ( summers fried my brain)
I've dotted ( i + j + k) with ( a + b +c ) and set it equal to 0 ending up with
a + b - c = 0 but i can't see a step on from there

In order for \(\displaystyle P : (a,b,c)\in \ell_1\) we need a value \(\displaystyle t=\alpha\) such that \(\displaystyle (a,b,c)=(8+\alpha, 12+\alpha, 14-\alpha)\).
Moreover, \(\displaystyle \overrightarrow {OP}\cdot<1,1,-1>=0\).
Can you carry on?

 

[H.Bisho18]

Think i got it thank you.

 

[pka]

Yes, you did do it. Well done.