Plane & 3D Vector Homework Solution

[lpbg]

Homework Statement

problem 1:
given the straight line r whose equation is r=<3+2t, 4+2t, -1-t>

0.Determine A, intersection of the plane yz
0.1the parameter value at A is t=
0.2therefore A=(...,...,...)

1.we want to re-parametrize r (be u the new parameter) so that:
1.1the new direction vector e be a unit vector, then e = <...,...,...>
1.2 as u increases the x coordinates increases. it follows that e=<...,...,...>
1.3 A be the new origin point. the new equation is: r=<...,...,...>

2. Determine B and C, intersections of r with the zx and xy plane respectively.
2.1 parameter values at the two points are Ub=... Uc=...
2.2 distances AB and AC are therefore dAB=... dAC=...
2.3 Points coordinates are B= (...,...,...) C=(...,...,...)

The Attempt at a Solution

A at x=0 hence 3+2t=0 therefore A at t=-3/2
point A(0,1,1/3)
direction vector d=(2,2,-1)

for 1.1 the formula to be applied is v/|v| but i don't know whether it should be applied to the direction vector or to the original equation. also question 1.2 is problematic for me since i don't understand what is asked for. any help is much appreciated

 

[verty]

For 1.1, if t increases, in what direction does the point r(t) travel? They want a unit vector in this direction.
For 1.2, you may need to flip that vector around so that it points toward the positive x axis.