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Quiz 1: Introduction to Vectors

Last unanswered question  Question  Next unanswered question
 

Question 1

 
 
Which of the following symbols represent vectors? Click on every option that does.
a) v   b) ---→ PQ
c) --→ 2u + AB   d) -v
e) u + v   f) 2u - 3v

 

There is at least one mistake.
For example, choice (a) should be true.
There is at least one mistake.
For example, choice (b) should be true.
This is the vector pointing in the opposite direction to --→ P Q.
There is at least one mistake.
For example, choice (c) should be true.
Both u and --→ AB are vectors, so their sum is also a vector.
There is at least one mistake.
For example, choice (d) should be true.
The negative of a vector is a vector pointing in the opposite direction.
There is at least one mistake.
For example, choice (e) should be true.
The sum of two vectors is a vector.
There is at least one mistake.
For example, choice (f) should be true.
Both 2u and -3v are vectors and their sum is also a vector.
Your answers are correct
  1. True.
  2. True. This is the vector pointing in the opposite direction to --→ P Q.
  3. True. Both u and --→ AB are vectors, so their sum is also a vector.
  4. True. The negative of a vector is a vector pointing in the opposite direction.
  5. True. The sum of two vectors is a vector.
  6. True. Both 2u and -3v are vectors and their sum is also a vector.
 

Question 2

 
 
How many different vectors are drawn here ? Enter your answer into the answer box.

 

Your answer is correct
Vectors are equal when they have the same direction and length; their position in space does not matter.
Not correct. You may try again.
Remember that a vector is specified by its direction and magnitude, so that the two arrows of equal length pointing to the west represent the same vector, while the three arrows of equal length pointing to the north-east also represent the same vector.
 

Question 3

 
 
How many different vectors are drawn here ?

 

Your answer is correct
All of the vectors are different. However, some of these vectors are scalar multiples of each other; for example,
= -
Not correct. You may try again.
Vectors are equal when they have the same direction and length; their position in space does not matter.
 

Question 4

 
 
Express the vector u in terms of a, b, c.
a b u c
a) -a + b + c   b) a-b + c
c) a + b + c   d) -a - b - c

 

Not correct. Choice (a) is false.
Trace out the vector u starting at the tail and moving along the vectors a, b and c until you reach the head of u.
Not correct. Choice (b) is false.
Trace out the vector u starting at the tail and moving along the vectors a, b and c until you reach the head of u.
Not correct. Choice (c) is false.
Trace out the vector u starting at the tail and moving along the vectors a, b and c until you reach the head of u.
Your answer is correct.
Starting at the tail of u, we see that u = -a - b - c.
 

Question 5

 
 
Express the vector u in terms of a, b, c.
a u c b
a) -a + b + c   b) a - b - c
c) a + b + c   d) -a - b - c

 

Not correct. Choice (a) is false.
Your answer is correct.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
 

Question 6

 
 
If [ ] --→ 3 OP = - 2 , [ ] --→ - 2 OQ = 1 and --→ --→ QP = AB, where B = (3,5), find A .
a) A = (2,- 8)   b) A = (- 2,- 8)
c) A = (- 2,8)   d) A = (- 1,8)
e) A = (- 2,7)

 

Not correct. Choice (a) is false.
First find -Q-P→. Then let A = (a,b) so that -Q-→P = --A→B = [ ] 3- a 5- b, and solve for a and b.
Not correct. Choice (b) is false.
First find -Q-P→. Then let A = (a,b) so that --→ QP = --→ AB = [3- a] 5- b, and solve for a and b.
Your answer is correct.
Not correct. Choice (d) is false.
First find --→ QP. Then let A = (a,b) so that --→ QP = --→ AB = [ ] 3- a 5- b, and solve for a and b.
Not correct. Choice (e) is false.
First find --→ QP. Then let A = (a,b) so that --→ QP = --→ AB = [3 - a] 5 - b, and solve for a and b.
 

Question 7

 
 
If A = (3,-1), B = (3,5) and C = (-2,0), find P such that -O-P→ = -A-→B + 2-B-→C.
a) P = (10,7)   b) P = (10,14)
c) P = (-10,-4)   d) P = (-20,-26)

 

Not correct. Choice (a) is false.
Find --→ AB and --→ BC first. Then find 2--→ BC and hence --→ OP.
Not correct. Choice (b) is false.
Find --→ AB and --→ BC first. Then find 2--→ BC and hence --→ OP.
Your answer is correct.
We have
--→ --→ --→ [0] [- 5] [- 10] OP = AB + 2BC = 6 + 2 - 5 = - 4 .
Hence P = (-10,-4).
Not correct. Choice (d) is false.
Find --→ AB and --→ BC first. Then find 2--→ BC and hence --→ OP.
 

Question 8

 
 
Relative to the origin, point P has position vector u and Q has position vector v. What is --→ QP ?
a) u - v   b) v - u
c) u + v   d) -u - v

 

Your answer is correct.
--→ --→ --→ QP = OP - OQ = u- v
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
 

Question 9

 
 
In 3D space, vectors u and v are defined as follows:
u = [3,5,- 1], v = [1,4,7].
If the tail of vector u + v is translated to the point P = (6,-2,1), which point corresponds to the head Q of u + v?
a) (4,9,6)   b) (10,7,7)
c) (0,0,0)   d) (-2,3,5)
e) (2,-11 - 5)

 

Not correct. Choice (a) is false.
Your answer is correct.
We find that u + v = [4,9,6] and if the coordinates of Q are (a,b,c) then u + v = -P-→Q = [a - 6,b + 2,c - 1]. This gives the result.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.
 

Question 10

 
 
Which vector is obtained when the vector expression
5(v- 2u)- 3(v- 4w )+ 3(u - v+ w)
is simplified?
a) -7u - v + 9w   b) -10u - v + 15w
c) -7u + v + 15w   d) -7u - v + 15w

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Your answer is correct.