Chapter 13 - Things to memorize

Question 1

(geometric)

v • w =

Answer 1

||v|| ||w|| cosΘ

Question 2

(Algebraic) (Assume 3 dimenstions)

v • w =

Answer 2

v₁w₁ + v₂w₂ + v₃w₃

Question 3

Is the dot product a scalar or vector?

Answer 3

Scalar

Question 4

What does the dot product represent? What does it mean if the dot product is big or small?

Answer 4

How alligned 2 vectors are. Bigger if more alligned, smaller if less

Question 5

Which of these 3 properties does the dot product have?

Commutative

Associative

Distrbutive

Answer 5

All three

Question 6

What is the equation when we take the dot product of perpendicular vectors?

Answer 6

v • w = 0

Question 7

What is the length of vector v in terms of the dot product?

Answer 7

||v|| = (v • v)^1/2

Question 8

What is the equation we get if we want to scale v down to a unit vector

Answer 8

v/||v|| (the resultant will have length 1)

Question 9

What is the projection equation for a parallel vector v_p?

Answer 9

v_p = [(v • u)/||v||^2]u

Question 10

What is the projection equation for a perpendicular vector v_perp?

Answer 10

v_perp = v - v_p

Question 11

The equation of the plane with normal vector n = ai + bj + ck and containing the point P₀ =(x₀, y₀, z₀) is…

Answer 11

a(x - x₀) + b(y - y₀) + c(z - z₀) = 0

or

ax + by + cz = 0

Question 12

a x b =

Answer 12