H Precalc Vectors Exam

Length/Magnitude/Speed of 2D Vector and 3D Vector

|v|=sqrt(a²+b²) || |w|=sqrt(a²+b²+c²)

Unit Vector

1/|v|*v (reciprocal of magnitude times vector)

Dot Product (useful for finding angles between vectors)

v*w = |v||w| cos theta

2D Line Equation / 3D Line Equation

(x,y) = (x1,y1) + t<a,b> || (x,y,z) = (x1,y1,z1) + t<a,b,c>

Cartesian Triple Equation

m1x+b1 = m2y+b2 = m3z + b3

Equation of a Plane

a(x-x0) + b(y-y0) + c(z-z0)

Area of Parallelogram (using cross product)

|v x w| (half of this is the area of triangle)

Area of Parallelogram (using sine)

|v||w|*sin theta (half of this is the area of triangle)

Finding a perpendicular vector of two vectors (perpendicular of AB and AC)

Cross product is the perpendicular vector (of AB and AC)

Distance between point and plane

Create parametric equations using “t” with point (use plane equation for vector). Plug into plane equation and solve for t. Then use t to vector and magnitude to find distance

Angle between planes

Find two vectors using plane equations. Use dot product to find angle between vectors

Find equation of plane from two points

Find cross product of the points and substitute one points coordinates + cross product to make plane equation