Vectors

Question 1

Give the equation for the vector projection of v₁ onto v₂

Answer 1

Question 2

Give the equation for the scalar projection of v₁ onto v₂

Answer 2

Question 3

Describe how to obtain a vector perpendicular to v1 and v2

Answer 3

v1 x v2

Question 4

Give the scalar equation of a line

Answer 4

Question 5

Give the vector equation of a line

Answer 5

Question 6

Give the equation for the smallest difference between a point C and a line that passes through A and B

Answer 6

Note that this is the same equation used to find the shortest distance between two lines

Question 7

Describe how to multiply two vectors using determinants

Answer 7

Question 8

Give the complex conjugate of r = e^i𝜃

Answer 8

r* = e^-i𝜃

Question 9

State how to convert between polar and cartesian coordinates

Answer 9

x = rcos𝜃

y = rsin𝜃