MCV4U_Unit#6_TCavers.docx - MCV4U: Lesson #16-17 Lines and...

MCV4U: Lesson #16-17 –
Lines and Planes (Part A)
Taylor Cavers
Student Number: 17144011

Lesson #17: Application of Vector Multiplication
Task #1: Knowledge and Understanding Questions
1. Find the angle between vectors
⃗ a =( 7,1, − 2 )
and
⃗
b =( 5,4,4 )
. (5 marks)
a
a b

cosθ =
31
√
3078
cosθ = 0.5588
θ = cos
− 1 (
0.5588
)
θ = 56.0 °
Therefore, the angle between vectors
⃗ a =( 7,1, − 2 )
and
⃗
b =( 5,4,4 )
is 56.0° and is
acute.
2. Find the cross product of
⃗ u =(− 2 , 3 , − 4 )
and
⃗ v =( 1, − 4,5 )
. (4 marks)
is
3. Given two vectors
⃗ u =( 5, − 1,5 )
and
⃗ v =(− 4,5,2 )
, find the projection of
⃗ u
⃗ v
in Cartesian form. (4 marks)
on

Proj
⃗ v
⃗ u =
(
4
3
, −
5
3
, −
2
3
)
Therefore, the projection of
⃗ u
on
⃗ v
in Cartesian form is
Proj
⃗ v
⃗ u =
(
4
3
, −
5
3
, −
2
3
)
.
4. Find the volume of a parallelepiped defined by the vectors
⃗ u =( 3,4, − 2 )
⃗ v =( 0,2,3 )
, and
⃗ w =(− 2,0, − 4 )
. (4 marks)
,
.

Therefore, the volume of a parallelepiped defined by the vectors
⃗ u =( 3,4, − 2 )
,
⃗ v =( 0,2,3 )
, and
⃗ w =(− 2,0, − 4 )
is
V = 56 cubic units
.