calc3 test1

Question 1

ca x b = ?

Answer 1

c(a x b) = a x cb

Question 2

(a + b) x c = ?

Answer 2

a x c + b x c

Question 3

a · (b x c) = ?

Answer 3

(a x b) · c scalar triple product

Question 4

a x (b x c)

Answer 4

(a ·c)b – (a · b)c vector triple product

Question 5

Parametric form equation of a line in R^3

Answer 5

r = r˳ + tv, r = , r˳ = , v =

Question 6

vector for for equation of a line in R^3

Answer 6

=

Question 7

symmetric for for equation of a line in R^3

Answer 7

(x-x˳)/a, (y-y˳)/b, (z-z˳)/c

Question 8

Vector equation of a plane

Answer 8

n ∙ (r – rₒ) n = , r = , rₒ =

Question 9

scalar equation of line

Answer 9

a(x-xₒ) + b(y-yₒ) + c(z-zₒ) = 0

Question 10

parabolic cylinder

Answer 10

Z = x²

Question 11

Ellipsoid

Answer 11

x²/a² + y²/b² + z²/c² = 1 standard form, must equal 1, always an ellipse no mater which way you slice it

Question 12

Hyperboloid one sheet

Answer 12

x²/a² + y²/b² - z²/c² = 1 standard form, must equal 1, neg vari will give axis, ellipse in one direction, hyperbolas in in the other direction

Question 13

Hperboloid two sheets

Answer 13

-x²/a² - y²/b² + z²/c² = 1 neg vari will give axis

Question 14

elliptic paraboloid

Answer 14

x²/a² + y²/b² - z/c = 0 odd out sign gives axis

Question 15

hyperbolic paraboloid

Answer 15

x²/a² - y²/b² - z/c = 1 odd out sign gives axis

Question 16

formula for distance between two planes

Answer 16

D = |ax1 + by1 + cz1 + d| / √(a2 + b2 + c2)