S3W4 Vectors and Polar Coordinate review

1

below are pairs of vectors written in different forms. Match the vectors on the left to their pair on the right.

Stavka koja se može prevući		Odgovarajuća stavka

		\vec{u} has an terminal point at (14,3) and an initial point at (8,-9)

		from the x-axis

1

To find the magnitude of a vector in component form, you simply

add the magnitudes of the components

use pythagorean theorem with the components

take the inverse tan of the coefficient of \hat{j} over the coefficient of \hat{i}

Divide the components by the angle

1

To find the angle of the vector from the horizontal axis,

add the magnitudes of the components

use pythagorean theorem with the components

take the inverse tan of the coefficient of \hat{j} over the coefficient of \hat{i}

Divide the components by the magnitude

1

To find the component form of the unit vector in the direction of a vector you simply

add the magnitudes of the components

use pythagorean theorem with the components

take the inverse tan of the coefficient of \hat{j} over the coefficient of \hat{i}

Divide the components by the magnitude

1

To find the dot product of two vectors you

multiply the \hat{i} components together and make that the coefficient of the \hat{i}, and multiply the \hat{j} components together and make that the coefficient of the \hat{j}

multiply the \hat{i} components together and multiply the \hat{j} components together and then add those products together.

multiply both components by the scalar

Multiply the \hat{i} component by the \hat{j} and vice-versa. then add them together

1

To find if two vectors are parallel you

determine the \frac{delta y}{delta x} of both vectors and see if they are equal

determine the \frac{delta y}{delta x} of both vectors and see if they are reciprocal of each other

take the dot product to determine if it is equal to 0

take the dot product to determine if it is equal to the magnitude of one of the vectors

1

To find if two vectors are perpendicular you

determine the \frac{delta y}{delta x} of both vectors and see if they are equal

determine the \frac{delta y}{delta x} of both vectors and see if they are reciprocal of each other

take the dot product to determine if it is equal to 0

take the dot product to determine if it is equal to the magnitude of one of the vectors

1

given two vectors in component form, you can find the angle between them by

take the inverse tan of \hat{i} components divided by the\hat{j} components and then add those angles

find the dot product using the component equation, divide by the product of the magnitudes of both vectors, then take the inverse cosine

using pythagorean theorem

graphing and using a protractor is the only way

1

When you are finding the component form of a vector \vec{u} given as a magnitude and an angle \theta from the positive x axis you would

||\vec{u}||\cdot\hat{i}+||\vec{u}||\hat{j}

<r\sin\theta, r\cos\theta>

<magnitude\cdot\cos\theta, magnitude\cdot\sin\theta>

1

Which of these is finding the component of \vec{u} along \vec{v}

(\vec{u}\cdot\hat{v})\hat{v}

both of the above will work

neither of the above will work

1

in polar coordinates r stands for

the x coordinate

the y coordinate

the distance between your point and the origin

the angle from the x-axis

1

in polar coordinates \theta stands for

the x coordinate

the y coordinate

the distance between your point and the origin

the angle from the x-axis

1

in polar coordinates r\cos\theta is the

the x coordinate

the y coordinate

the distance between your point and the origin

the angle from the x-axis

1

in polar coordinates r\sin\theta is the

the x coordinate

the y coordinate

the distance between your point and the origin

the angle from the x-axis

1

when converting a polar equation into a rectangular equation I simply

Replace x and y with r\cos\theta and r\sin\theta respectively and then solve for r

Replace x and y with r\cos\theta and r\sin\theta respectively and then solve for \theta

replace r and \theta with \sqrt{x^2+y^2} and \tan^{-1} respectively then solve for y

replace r and \theta with \sqrt{x^2+y^2} and \tan^{-1} respectively then simplify, possibly using completing the square to consolidate x terms and y terms

1

What does De Moivre's Theorem relate?

Angles and trigonometry

Real numbers and polynomials

Complex numbers and powers

Vectors and magnitudes

1

Which formula represents De Moivre's Theorem?

a^n + b^n = (a + b)^n

\sin^2 x + \cos^2 x = 1

(\cos \theta + i\sin \theta)^n = (\cos n\theta + i\sin n\theta)

a^2 + b^2 = c^2

1

In De Moivre's Theorem, 'n' represents what?

Any integer

Rational numbers

Only odd numbers

Only even numbers

1

De Moivre's Theorem applies to which type of numbers?

Real numbers

Rational numbers

Whole numbers

Complex numbers

1

S3W4 Vectors and Polar Coordinate review

below are pairs of vectors written in different forms. Match the vectors on the left to their pair on the right.

To find the magnitude of a vector in component form, you simply

To find the angle of the vector from the horizontal axis,

To find the component form of the unit vector in the direction of a vector you simply

To find the dot product of two vectors you

To find if two vectors are parallel you

To find if two vectors are perpendicular you

given two vectors in component form, you can find the angle between them by

When you are finding the component form of a vector \vec{u} given as a magnitude and an angle \theta from the positive x axis you would

Which of these is finding the component of \vec{u} along \vec{v}

in polar coordinates r stands for

in polar coordinates \theta stands for

in polar coordinates r\cos\theta is the

in polar coordinates r\sin\theta is the

when converting a polar equation into a rectangular equation I simply

What does De Moivre's Theorem relate?

Which formula represents De Moivre's Theorem?

In De Moivre's Theorem, 'n' represents what?

De Moivre's Theorem applies to which type of numbers?

You have an aleks assignment - it is optional. work on it and then report back here - what questions do you think you would like to work on in class?

below are pairs of vectors written in different forms. Match the vectors on the left to their pair on the right.

To find the magnitude of a vector in component form, you simply

To find the angle of the vector from the horizontal axis,

To find the component form of the unit vector in the direction of a vector you simply

To find the dot product of two vectors you

To find if two vectors are parallel you

To find if two vectors are perpendicular you

given two vectors in component form, you can find the angle between them by

When you are finding the component form of a vector \vec{u} given as a magnitude and an angle \theta from the positive x axis you would

Which of these is finding the component of \vec{u} along \vec{v}

in polar coordinates r stands for

in polar coordinates \theta stands for

in polar coordinates r\cos\theta is the

in polar coordinates r\sin\theta is the

when converting a polar equation into a rectangular equation I simply

What does De Moivre's Theorem relate?

Which formula represents De Moivre's Theorem?

In De Moivre's Theorem, 'n' represents what?

De Moivre's Theorem applies to which type of numbers?

You have an aleks assignment - it is optional. work on it and then report back here - what questions do you think you would like to work on in class?