Vectors Unit Assignment- Calculus and Vector - VHS - MCV4U

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MCV4U k1+, Calculus and Vector, 12, University Virtual High School
Unit Assignment: Vectors Unit Assignment
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Question 1
1. State whether each quantity is a vector or
scalar. Explain.
a. Speed
b. Velocity
c. Weight
d. Mass
e. Area
Answer 1
(a) Speed is a scalar as a scalar has only magnitude no direction
As, we know, speed = distance/time it has magnitude no direction
s =
d
t
(b) Velocity is a vector quantity. We specify velocity with magnitude in a
specific direction.
Hence velocity y=
𝑑
𝑡
has both magnitude and direction.
(c) Force = mass x acceleration = weight.
Hence, force is a product of mass (scalar) and acceleration (vector)
Therefore, weight is a vector product it has both direction and
magnitude.
(d) ‘mass’ is only scalar quantity as its just a magnitude and material
which makes it a scalar.
(e) Area is a scalar. Area is measured in space.it has magnitude no
direction.

Question 2
In the diagram below, ABEF, BCDE and FEHG are
parallelograms.
𝐴𝐵= u and 𝐴𝐹 = v
a. Write the following vectors in terms of u and
v:
i. 𝐴𝐸
ii. 𝐴𝐷
iii. 𝐹𝐶
iv. 𝐵𝐺
b. Give an example of a vector that is equal to:
v. 2u
vi. u - 2v
Answer 2
(a) (i) 𝐴𝐸 = 𝐴𝐵 + 𝐵𝐸
𝐵𝐸 = 𝐴𝐹 + 𝑉
Also, 𝐴𝐵 = 𝑢
𝐴𝐸 = 𝑉 + 𝑢
(iii) 𝐹𝐶 = 𝐹𝐷 +𝐷𝐶
𝐹𝐷 = 𝐴𝐶 = 𝐴𝐵+𝐵𝐶 = 𝑉 + 𝑢 = 2𝑢
𝐷𝐶 = -𝐶𝐷 = -𝐴𝐹 = -𝑉
𝐹𝐶 = 2𝑢 - 𝑉
(iv) 𝐵𝐺 = 𝐵𝐻 + 𝐻𝐺
𝐵𝐺 = 𝐵𝐸 + 𝐸𝐻+ 𝐻𝐺 (as 𝐵𝐸 = 𝐴𝐹 and 𝐸𝐻 =𝐸𝐺)
𝐵𝐺 = 𝐴𝐹+𝐴𝐺+𝐻𝐺 (𝐻𝐺 = 𝐵𝐴 = u)
𝐵𝐺 = 𝑉 = 𝑉 + 𝑢
𝐵𝐺 = u + 2𝑉
(ii) (a) 2𝑢  u + u
We can consider
𝐴𝐶 and 𝐹𝐷 as
𝐴𝐶 = 𝐹𝐷 = 𝑢 + 𝑢 = 2𝑢
(b) u - 2𝑉
= u + (-𝑉-𝑉)
𝐺𝐵 = 𝐻𝐵 +𝐻𝐺 as, 𝐻𝐵 = 𝐻𝐸 + 𝐸𝐵
= -2V + u = -V-V
= 𝑢-2𝑉 = -2V
𝐻𝐺 = u = 𝐴𝐵
(ii) 𝐴𝐷 = 𝐴𝐵 + 𝐵𝐶 + 𝐶𝐷
As we know, 𝐴𝐵 = 𝐵𝐶 = 𝑢
𝐶𝐷 = 𝐴𝐹 = 𝑉
𝐴𝐷 = 𝑢 + 𝑢 + 𝑉 = 2𝑢 + 𝑉

Question 3
Draw diagrams to show two vectors a and b, and
the vectors a + b and a - b.
a. When is the magnitude of a + b more than
that of a - b?
b. When is the magnitude of a + b less than that
of a - b?
c. When is the magnitude of a + b equal to that
of a - b?
d. When is |a + b| = |a| + |b|?
e. What is the minimum value of |a + b|?
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Question 4
A boat sails 5 km North, then 3 km Northeast.
Use trigonometry to find the boat's distance and
bearing from its starting point. Please contact to get complete assignment - admin@panhelp.com

Question 5
Convert the following vectors;
a. 50 m on a bearing of 222° to Cartesian form
b. [4, -9] to direction/magnitude form

Question 6
Express as a single vector:
a. 𝐴𝐸 𝐸𝐶
b. 𝐹𝐵 𝐴𝐵
c. 𝑇𝑉 - 𝑇𝑆 + 𝑃𝑄 - 𝑆𝑄

Question 7
Demonstrate using diagrams;
a. That vector addition is commutative ie. a + b =
b + a
b. That vector addition is associative ie. a + (b +
c) = (a +b) + c

Question 8
Research an example of the use of vectors, and
explain how the mathematics is used, for
example in engineering, computer animation,
gaming, 3-D printing or GPS technology

Vectors Unit Assignment- Calculus and Vector - VHS - MCV4U

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