9/16/2019
Nanyang Technological University - Production -
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19S1 Mathematics 1,
MSE BARIQ HIBATULLAH NURLIS, 9/14/19 at 5:34:27 PM SGT
Question1: Score 0.66/1
2
⎛
Let u
= ⎜
⎝
2
−4
⎞
⎟
⎛
and v
3
⎞
= ⎜ −1 ⎟
⎠
⎝
2
. Find
⎠
(a) the magnitude of u, express your answer up to 2 decimal places.
Answer :
Your response
4.89

Correct response
4.90
Grade: 1/1.0
.
(b) the dot product of u and v .
Answer :
Your response
-4

Correct response
-4
Grade: 1/1.0
.
(c) the angle between u and v , give your answer in radians, up to 2 decimal places.
Answer :
Your response
102.6

Correct response
1.79
Grade: 0/1.0
.
 Total grade: 1.0×1/3 + 1.0×1/3 + 0.0×1/3 = 33% + 33% + 0%
Question2: Score 1/1
Let a, b and c be unit vectors such that a ⋅ b
,b⋅c
= 1/5
and a ⋅ c
. Evaluate (write in the exact form)
= 1/8
=
||2a||

= 1/2
Your response
2
Correct response
Your response
5
Correct response
Your response
3/8
Correct response
Your response
1/8 - 1/5
Correct response
Grade: 1/1.0
2a ⋅ 5b =

Grade: 1/1.0
a ⋅ (b − c) =

Grade: 1/1.0
(a + b + c) ⋅ (a − b) =

Grade: 1/1.0
 Total grade: 1.0×1/4 + 1.0×1/4 + 1.0×1/4 + 1.0×1/4 = 25% + 25% + 25% + 25%
Question3: Score 1/1
If ||u||
= 2
, ||v||
= 3
and u ⋅ v
= 3
, find ||u + 2v|| , express your answer up to 2 decimal places.
Answer :
Your response
7.22

Correct response
Grade: 1/1.0
.
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9/16/2019
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 Total grade: 1.0×1/1 = 100%
Question4: Score 1/1
Let u and v be vectors where ||u + v||
= 4
and ||u − v||
= 7
. Find u ⋅ v .
Answer :
Your response
Correct response
-33/4

Grade: 1/1.0
 Total grade: 1.0×1/1 = 100%
Question5: Score 0/1
Consider two vectors a
and b , find x, y and z .
= −4i − j
and b
= 4i + j + k
. If c
= xi + yj + kz, x > 0
is the unit vector that is perpendicular to both a
Answer :
x =

Your response
No answer
Correct response
1/17*17^(1/2)
Your response
No answer
Correct response
-4/17*17^(1/2)
Your response
No answer
Correct response
0
Grade: 0/1.0
y =

Grade: 0/1.0
z =

Grade: 0/1.0
 Total grade: 0.0×1/3 + 0.0×1/3 + 0.0×1/3 = 0% + 0% + 0%
Question6: Score 0/1
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Question7: Score 0/1
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Question8: Score 0/1
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Question9: Score 0/1
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Question10: Score 0/1
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Question11: Score 0/1
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Question12: Score 0/1
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Question13: Score 0/1
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Question14: Score 0/1
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Question15: Score 0/1
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