Question

6. Consider the three points in R^3: A (3, 2, 0), B (0, 4, 2), and C (1, 0, 5).
(a) The two vectors ⃗u and ⃗v both begin at A and point to B and C, respectively.
Calculate ⃗u and ⃗v.
(b) Determine the angle between ⃗u and ⃗v.
(c) Calculate the area of the parallelogram determined by ⃗u and ⃗v.
(d) Determine the vector equation of the line which passes through the points B
and C.

Answer 1

a) AB= b-a
AC= c-a

Answer 2

that will give you the two vectors u and v

Answer 3

then to find the angle between you will have to use the dot product
u*v=\[\left| u \right|\left| v \right|\cos \theta\]