Vector

Question 1

Find equation of the line that pass through A (1, 2, 3) and B (4, 5, 6).

Answer 1

i + 2j + 3k + w (vector AB).

Vector AB = OB -OA.

Question 2

Show that 2 lines not intersect (skew).

Answer 2

Expand 2 equation to ijk form.

Compare ijk to find w and m.

Not all the w and m are same.

Question 3

Turn vector equation to cartesian equation.

Answer 3

Nr = Nr
Position vector × direction vector = position vector x direction vector
Ijk x ijk = (xi×yj+zk) x ijk
ixi + jxj + kxk = xyz
Value = xyz
Xyz = value

Question 4

Find intersecting point between line and plane.

Answer 4

Find general form of line.
Sub lamda into plane equation to get lamda.
Use lamda sub into line equation to find position vector.