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s3w3 review for test
By Gwyneth Lenfest
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Last updated 5 months ago
22 questions
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Question 1
1.
What is the result of adding two vectors with the same magnitude and opposite directions?
The zero vector
The sum of their magnitudes
The difference of their magnitudes
Their product
Question 2
2.
If two vectors are orthogonal, what can be said about their dot product? a) It is zero b) It is positive c) It is negative d) It is undefined
It is zero
It is positive
It is negative
it is the negative reciprocal.
Question 3
3.
If the magnitude of a vector is doubled, how does it affect its components in rectangular coordinates?
The x and y components are halved
The x and y components are doubled
Only the x component is doubled
Only the y component is doubled
Question 4
4.
When multiplying a vector by a positive scalar, what happens to its direction?
It is reversed
It remains the same
It becomes orthogonal
It becomes undefined
Question 5
5.
When multiplying a vector by a negative scalar, what happens to its direction?
It is reversed
It remains the same
It becomes orthogonal
It becomes undefined
Question 6
6.
Which of the following represents the projection of vector \vec{v} onto vector \vec{w}?
∣\vec{w}∣cos(
θ
)\hat{v}
∣\vec{v}|cos(
θ
) \hat{w}
∣\vec{v}∣sin(
θ
)\hat{w}
∣\vec{w}∣sin(
θ
)\hat{v}
Question 7
7.
How are \vec{m} and \hat{m} similar and how are they different?
Question 8
8.
What is the equation that tells you the magnitude of vector a\hat{i}+b\hat{j}
Question 9
9.
the magnitude you gave the equation for above is a
dot product
orthogonal product
scalar
vector
Question 10
10.
If the dot product of two vectors is zero, what can be concluded about the angle between them?
They are parallel
They are collinear
The angle cannot be determined
They are perpendicular
Question 11
11.
In polar coordinates, what does the angle
θ
represent?
The radius of the point
The angle between the ray from the origin to the point and the x-axis
The distance from the point to the x-axis
The distance from the point to the y-axis
Question 12
12.
How would the polar coordinates (
r
,
θ
) change if the point is reflected across the x-axis?
r
becomes −
r
,
θ
remains the same
r
remains the same,
θ
becomes −
θ
r
remains the same,
θ
remains the same
r
becomes −
r
,
θ
becomes −
θ
Question 13
13.
If a point is given in Cartesian coordinates as (
x
,
y
), what are its polar coordinates?
(x,y)
Question 14
14.
If a point is in polar coordinates (
r
,
θ
), how does doubling
r
affect the location of the point?
It moves the point twice as far from the origin
It changes the angle θ to 2θ
It reflects the point across the y-axis
It reflects the point across the x-axis
Question 15
15.
If
and
, what is the product
in polar form?
6(cos
π
/2+
i
sin
π
/2)
6(cos
π
/6+
i
sin
π
/6)
6(cos
π
/3+
i
sin
π
/3)
6(cos
π
+
i
sin
π
)
Question 16
16.
What is the magnitude of the complex number
z
=3−4
i
given in Cartesian form?
5
7
32+(−4)232+(−4)2
32⋅(−4)232⋅(−4)2
Question 17
17.
What is the polar equation for a circle centered at the origin with radius r=a?
\theta = a
r = a^2
r = a
r = 2a
Question 18
18.
What would be the polar representation of the Cartesian point (2, 2)?
r = 2, \theta = \frac{\pi}{2}
r = 2, \theta = \frac{\pi}{4}
r = \sqrt{2}, \theta = \frac{\pi}{2}
r = 2\sqrt{2}, \theta = \frac{\pi}{4}
Question 19
19.
Which quadrant would the point (r=3, \theta = \frac{3\pi}{4}) be located in the polar coordinates system?
3rd Quadrant
4th Quadrant
2nd Quadrant
1st Quadrant
Question 20
20.
If a point moves from
what path does it trace in the plane?
Half-circle in counter-clockwise direction
Straight line from (1,0) to (1,1)
Full circle centred at origin
Half-circle in clockwise direction
Question 21
21.
3cis\theta is the same as
Question 22
22.
is the same as