Let A=(2,8,5)
B=(6,0,3)
C=(4,7,9)
1.Find the vectors
a.) u=⃗
BA
2. Give examples of vectors which are parallel to u, v and w respectively.
3. Find a vector which is orthogonal to
a. u and v
4. Find the angle between and determine if they are parallel(perpendicular) or not
a. u and v
5. Find the projection of
a. u onto v
6. Find Orthogonal projection of
a. u onto v
7. Find the area of the triangle with vertices A,B and C,
8. Find the area of the parallelogram formed by
a. u and v
9.. Find the volume of the parallelpiped formed by
a. u ,v and uxv
10.Define the following Terms and give example for each
a. Symmetric Matrix
b. Skew-symmetric Matrix
c. Lower-Triangular Matrix
d. Upper Triangular Matrix
11. Write as a sum of symmetric and skew-symmetric matrices.
a.)
(
2 5 0 6 8 3 4 9 )
12. Solve the system 4 x+3 y+2 z=3
2 x+5 y+z=2
2 x+ y+6 z=5
using
a. Cramer’s rule
b. Inverse method
c. Gaussian Elimination
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