s3w3 review for test

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

1

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.

1

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

1

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

1

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

1

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}

1

How are \vec{m} and \hat{m} similar and how are they different?

1

What is the equation that tells you the magnitude of vector a\hat{i}+b\hat{j}

1

the magnitude you gave the equation for above is a

dot product

orthogonal product

scalar

vector

1

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

1

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

1

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

1

If a point is given in Cartesian coordinates as (x,y), what are its polar coordinates?

(x,y)

1

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

1

If
and
, what is the product
in polar form?

6(cosπ/2+isinπ/2)

6(cosπ/6+isinπ/6)

6(cosπ/3+isinπ/3)

6(cosπ+isinπ)

1

What is the magnitude of the complex number z=3−4i given in Cartesian form?

5

7

32+(−4)232+(−4)2

32⋅(−4)232⋅(−4)2

1

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

1

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}

1

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

1

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

1

3cis\theta is the same as

1

s3w3 review for test

What is the result of adding two vectors with the same magnitude and opposite directions?

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

If the magnitude of a vector is doubled, how does it affect its components in rectangular coordinates?

When multiplying a vector by a positive scalar, what happens to its direction?

When multiplying a vector by a negative scalar, what happens to its direction?

Which of the following represents the projection of vector \vec{v} onto vector \vec{w}?

How are \vec{m} and \hat{m} similar and how are they different?

What is the equation that tells you the magnitude of vector a\hat{i}+b\hat{j}

the magnitude you gave the equation for above is a

If the dot product of two vectors is zero, what can be concluded about the angle between them?

In polar coordinates, what does the angle θ represent?

How would the polar coordinates (r,θ) change if the point is reflected across the x-axis?

If a point is given in Cartesian coordinates as (x,y), what are its polar coordinates?

If a point is in polar coordinates (r,θ), how does doubling r affect the location of the point?

If and , what is the product in polar form?

What is the magnitude of the complex number z=3−4i given in Cartesian form?

What is the polar equation for a circle centered at the origin with radius r=a?

What would be the polar representation of the Cartesian point (2, 2)?

Which quadrant would the point (r=3, \theta = \frac{3\pi}{4}) be located in the polar coordinates system?

If a point moves from what path does it trace in the plane?

3cis\theta is the same as

is the same as

What is the result of adding two vectors with the same magnitude and opposite directions?

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

If the magnitude of a vector is doubled, how does it affect its components in rectangular coordinates?

When multiplying a vector by a positive scalar, what happens to its direction?

When multiplying a vector by a negative scalar, what happens to its direction?

Which of the following represents the projection of vector \vec{v} onto vector \vec{w}?

How are \vec{m} and \hat{m} similar and how are they different?

What is the equation that tells you the magnitude of vector a\hat{i}+b\hat{j}

the magnitude you gave the equation for above is a

If the dot product of two vectors is zero, what can be concluded about the angle between them?

In polar coordinates, what does the angle θ represent?

How would the polar coordinates (r,θ) change if the point is reflected across the x-axis?

If a point is given in Cartesian coordinates as (x,y), what are its polar coordinates?

If a point is in polar coordinates (r,θ), how does doubling r affect the location of the point?

If and , what is the product in polar form?

What is the magnitude of the complex number z=3−4i given in Cartesian form?

What is the polar equation for a circle centered at the origin with radius r=a?

What would be the polar representation of the Cartesian point (2, 2)?

Which quadrant would the point (r=3, \theta = \frac{3\pi}{4}) be located in the polar coordinates system?

If a point moves from what path does it trace in the plane?

3cis\theta is the same as

is the same as

If
and
, what is the product
in polar form?

If a point moves from
what path does it trace in the plane?

If
and
, what is the product
in polar form?

If a point moves from
what path does it trace in the plane?