8. Vectors Flashcards
1
Q
Scalar Product
A
Multiplying corresponding terms and getting a sum of the products
i.e. (a₁ x b₁) + (a₂ x b₂) (+ (a₃ x b₃)) = Scale Product = a.b
2
Q
Acute angle between two vectors
A
Cosθ = a.b/(|a||b|)
3
Q
Scalar product of perpendicular lines
A
a.b = 0 (a and b being the vectors of said lines)
4
Q
Vector Equation of a Straight Line - position vector and parallel
A
r = a + λd
- r is the position vector for a general point on the line
- d is the direction vector
- a is the position vector of a known point on the line
5
Q
→
What does the vector AR mean?
A
→
AR = r - a, where r and a are position vectors of R and A respectively
6
Q
Vector equation of a Straight Line - two points
A
r = c + λ(d -c)
7
Q
Vector equation of a plane
A
r = a + λb + μc
8
Q
Cartesian equation of a line
A
If a = (a1 a2 a3) and b = (b1 b2 b3), r = a + λb:
x - a1)/b1 = (y-a2)/b2 = (z-a3)/b3 (= λ
