# SOLUTION: MCV4U Calculus Practice Quadrant Bearings Quiz

SOLUTION: MCV4U Calculus Practice Quadrant Bearings Quiz.

Name: ___________________________

/1 K/U

/ APP

/ COMM

/T/I

/

MCV4U –)LQDO3URMHFW3DUW

1. Convert each of the true bearings below into quadrant bearings: [COMM 1 mark each]

a) 075o

b) 128o

c) 234o

d) 317o

2. Convert each of the quadrant bearings below into true bearings: [COMM 1 mark each]

a) S56oE

b) S23oW

c) N71oW

d) N43oE

3. Vectors !, !, and ! are given below. Accurately draw the following vectors. [K/U 3

marks each]

!

a) ! = 2! − ! − !

!

!

!

!

b) ! = ! − 2! + !

!

!⃑

!⃑

!!⃑

4. Consider the parallelogram PQRS, where !” = ! and !” = !. Find a single vector to

represent each of the following: [APP 1 mark each]

a) ! + !

P

Q

b) ! + !

c) ! − !

d) ! − !

S

R

5. In the rectangular prism, find a vector expression, in term of !, !, and !, for each vector

below. [K/U 1 mark each]

a) !” =

b) !” =

c) !” =

d) !” =

!⃑

e) !” =

f) !” =

!⃑

!

!⃑

‘XH’DWH0DVW

Name: ___________________________

6. While camping in northern regions at night, people often keep food out of the reach

of animals by hanging it between two trees. If a food bag weighing 435 N is tied

between two trees 6 m apart by two ropes that are 4 m and 5 m long. Find the tension

in each rope. [T/I 4 marks]

A log is being pulled along level ground by a 370 N force exerted at an angle of 35° to

the ground. Find the magnitude of the force in the direction of motion and of the force

tending to lift the log. [APP 3 marks]

. A cruise ship’s captain sets the ship’s velocity to be 26 knots at a heading of 080°. The

current is flowing towards a bearing of 153° at a speed of 8 knots.

a) Draw a vector diagram to represent this situation. [APP 2 marks]

b) What is the ground velocity and bearing of the cruise ship? [APP 4 marks]

Name: ___________________________

‘XH’DWH0DVW

9. Determine ݇ so that [11,3, 2݇] is orthogonal (perpendicular) to [݇, 4, ݇]. [APP 2 marks]

10.Identify the type of triangle with vertices A(2,3, -5), B(-4, 8, 1) and C(6, -4, 0). [APP 3 marks]

11. Determine the projection of ݃റ ൌሾͳͲǡെ͵ǡ2] onto ݄ሬറ ൌሾͶǡെͶǡͳሿ. [K/U 2 marks]

12.If ܿറ = ܽറ × ܾሬറ, what is the value of ܿറ ή ܽറ and ܿറ ή ܾሬറ? Justify your response. [COMM 3 marks]

Name: ___________________________

‘XH’DWH0DVW

13. A wrench is rotated with torque of magnitude 100 Nym. The force is applied 30 cm

from the fulcrum, at an angle of 40°. What is the magnitude of the force? [APP 3 marks]

ሬሬሬሬሬറ on the three

14. Plot the points (ܣ3, 5, 7) and( ܤെ2, 0, െ1) and then plot the vector ܤܣ

dimensional plane as well. [COMM 3 marks].

15. Find the volume of the parallelepiped defined by ݑ

ሬറ = [1, 1, 9], ݒറ = [0, 0, 4], and ݓ

ሬሬറ =

[െ2, 0, 5]. [APP 3 marks]

16.A triangle has vertices A(3, 2, -5), B(4, -1, 7), and C(-8, 3, -6). Calculate the area of ‘ABC. [T/I

3 marks]

Purchase answer to see full

attachment