ENGR 2520 EXAM GUIDE- UNIVERSITY OF ONTARIO WINTER 2026

TUTORIAL 1
Q1. If vectors A = 5ax - 2ay + 6az and B = 3ax + ay. Find:

a) The component of B along ax;

b) The magnitude of 2A – B;
c) A unit vector along A + 2B.

Q2. Points P and Q are located at (0, 3, 5) and (-2, 2, 5). Calculate:
a) The position vector P and Q;
b) The distance vector from P to Q;
c) Distance between P and Q.
d) A vector parallel to PQ with magnitude of 5


Q3. Points P (2, -3, 5), Q (3, 4, 6) and R (1, 0, 8). Find
a) The position vector P and R;
b) The distance vector from Q to R;
c) Distance between Q and R.


Q4. Given vectors A = 2ax + 3ay + 5az and B = 2ay - 3az. Find
the angle between A and B.

, Q5. Three field quantities are given by
P = 2ax - ay, Q = 3ax - ay + 2az and R = 2ax - 3ay + az.

a) (P + Q)  (P - Q);
b) Q . R  P;
c) P . Q  R;
d) sin QR;

e) P  (Q  R);
f) A unit vector perpendicular to both Q and R;
g) The component of P along Q.


Q6.