General Physics (PHYS2226)
Geology, Mining and Environmental Science - GENV
Semester: Second Semester
Level: 200
Year: 2018
REPUBLIC OF CAMEROON REPUBLIQUE DU CAMEROUN
Peace-Work-Fatherland Paix-Travail-Patrie
MINISTER OF HIGHER EDUCATION MINISTERE DE L’ENSEIGNEMENT SUPERIER
THE UNIVERSITY OF BAMENDA UNIVERSITE DE BAMENDA
FACULTY OF SCIENCE FACULTE DES SCIENCES
PHYS2226: General Physics
Tutorial Sheet 1: VECTORS
1. Consider a particle moving around a square ABCD of sides 3 m. Determine the displacement of the
particle in moving from A to D, A to C, A to B and A to A through B, C and D.
2. Write out a multiplication table for the scalar products and vector products of all possible pairs of unit
vectors
3. Given two vectors:
(a) A = 2i + 2j and B = 3i - 3j
(b) A = 3i – 5j and B = 5i + 3j
i. Find the magnitude of each vector
ii. Find the vector sum and vector difference of the two vectors
iii. find their scalar product
iv. Find the unit vector in the direction of A
4. Consider two vectors
A = -2i + 2j + 5k and B = i + 3j – 2k
(a) Find the magnitude of each vector
(b) Write down an expression for the vector sum and find its magnitude.
(c) Compare the vector sum A + B and the vector difference A – B
(d) Find their scalar product and the vector product A x B
(e) Find the product A. (B x C) if C = A
5. Find the angle between the following 2 vectors:
(a) A = 2i + 3j + 5k and B = 3i + 4j – 5k
(b) A = 4i + 4j and B = -4i – 4j
6. A car moves 3 Km at 30
o
north-east, 1 Km east then 2 Km north. Find the distance of the car from the
starting point. What is the position of the car? In what direction is the car heading?
7. A vector A has a magnitude of 6 and lies in the position x-direction. Vector B has a magnitude of 4 and
lies on the xy-plane at an angle of 30
o
to the positive x-direction. Find the vector product of A and B
8. when two vectors A and B are drawn from a common point, the angle between them is Ѳ. Show that the
magnitude of their vector sum is (A
2
+ B
2
+ 2ABCosѲ)
1/2
.
9. Find a similar expression for the magnitude of A – B in (8) above.
10. Prove that for any three vectors A, B and C. A. (B x C) = (A x B). C
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