Dot Product and Cross Product

The dot product is 2 vectors multiplied together to get what type of quantity?

A scalar

The cross product is 2 vectors multiplied together to get what quantity?

A vector

What are the other 2 ways the dot product can be written?

A(Bcosa) or B(Acosa) - when you make a component of B along the direction of A or make a component of A along the direction of B. - then draw a perpendicular line making a 90° angle down to the other vector

What is the formula for the cross product using x and y components?

AxB = (AxBy-AyBx) k^ The answer will have k (hat) (K is the component vector for the 3rd dimension z)

What is the equation for the cross product of 2 vectors?

AxB =ABsina

How to find the dot product when you know the x & y components - WHATS the formula?

A•B = (AxBx)+(AyBy) 2 x components multiplied + 2 y components multiplied

What is the equation for the dot product?

A•B=ABcosa Where A is the magnitude of vector A B is the magnitufe of vector B Cosa is the cosine of angle alpha (a)

True or False: the order in which you multiply doesn't matter for the cross product.

False- order matters, when you multiply one way and then flip them it becomes negative

Fill in the blank: The cross product is ________________ to the plane of AxB

Perpendicular (3D)

When the angle of the two vectors is parallel or anti parallel what does the cross product equal?

The cross product = 0 because sine of 0° and 180° is 0

When a= 90° in the cross product, what will the cross product be?

The cross product will be: AxB =AB because the sine of 90° is just 1

How to distinguish the dot product from the cross product?

The dot product has a • between the 2 vectors being multiplied, The cross product has a x between the 2 vectors being multiplied

What will the dot product be when the 2 vectors multiplied are parallel to eachother?

The dot product will just be AB (magnitude of A times magnitude of B) because parallel vectors have an angle of 0° and the cosine of 0° is 1 so A•B= AB

What will the magnitude of the cross product be when the angle is acute (less than 90°) or obtuse (more than 90°)?

The magnitude will be less than AB but still positive

True or False: the cross product will always be positive because the sine of anything from 0° to 180° is positive

True!!!

What does it mean when vectors are anti parallel and what happens to the dot product when the vectors are anti parallel?

Vectors that are anti paralell are vectors that make a 180° angle pointing away from eachother. The cosine of 180° is -1 so dot product is: A•B= -AB

When will the dot product equal a positive number, equal zero, and equal a negative number?

When the angle is less than 90° the dot product will be positive. When the angle is 90° the dot product = 0. When the angle is greater than 90°, the dot product will be a negative number.