HI I want to check if my answers are right here, I can't do the last part so I believe my answers in the previous parts must be wrong..
Points A,B,C,D have the following coordinates
A1,3,1) B1,2,4) C2,3,6) D5,-2,1)
ai.) Evaluate the vector product, giving your answers in terms of the unit vectors i,j,k.
I found AB and AC and got -5i, 3j and 1k from doing the cross product.
aii.) Find the area of the triangle ABC.
I took the magnitude of the cross product result in ai.) and halved it, getting (1/2)sqrt(35)units^2
b.) The plane containing the points A,B, C is denoted by pi and the line passing through D perpendicular to pi is denoted by L. The point of intersection of L and pi is denoted by P.
bi.) FInd the cartesian equation of pi.
AB is the direction vector of pi, I thought. And then I'll need a point so
I got x=1, y=3-t, z=1+3t
bii.) FInd the cartesian equation of L.
The result of the cross product in ai.) is the direction vector of L, I thought. Dotting it by the direction vector of pi, I will get a zero.
So my answer was
x=5-5t, y=-2+3t, z=1+t
c.) Find the coordinates of P.
This is where I know my previous answers are wrong. I though to equate all the x, y and z values of L and pi. I get different values for t each time...
Please help me out!