SOLUTION: MCV4U Calculus Practice Quadrant Bearings Quiz

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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) !” =
!⃑
!
!⃑

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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]

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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]

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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]

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