SECTION 7.4 Flashcards
How do you get the component form of a vector for initial point A = (a₁, a₂) and point B = (b₁, b₂)?
<b₁-a₁, b₂-a₂>
How do you find the magnitude of a vector?
square root of (v₁)² + (v₂)²
How do you find the magnitude of two vectors added/subtracted together?
- Solve for standard form.
- Use the standard form for the new vector in the magnitude formula.
How do you find the unit vector of a given vector?
(1/magnitude)*vector
What is the component form of standard unit vector i?
<1, 0>
What is the component form of standard unit vector j?
<0, 1>
How do you solve for v₁ and v₂ with cosine and sine?
v₁ = |v|cosθ; v₂ = |v|sinθ
How do you find the direction vector of an angle?
tanθ = v₂/v₁
When do you use arctangent when solving for direction angles?
for vectors in the second quadrant
How do you get the dot product of <v₁, v₂> and <u₁, u₂>?
v₁u₁ + v₂u₂
How do you find the magnitude of a vector using dot product?
vector * vector = vector² = magnitude
How do you find the angle between vectors u and v?
cosθ = (vectors uv)/(magnitudes uv)
When are vectors u and v orthogonal?
when u*v = 0
