(incorrect) Find a vector parametric equation r rightarrow (t) for the line thro

Question

(incorrect) Find a vector parametric equation r rightarrow (t) for the line through the points P = (-5, -2, -4) and Q = (-5, 3, 1) for each of the given conditions on the parameter t. If r rightarrow (0) = -5, -2, -4 and r rightarrow (6) = -5, 3, 1 , then r rightarrow (t) = _____________ If r rightarrow (5) = P and r rightarrow (7) = Q, then r rightarrow (t) = ______________ If the points P and Q correspond to the parameter values t = 0 and t = -4, respectively, then r rightarrow (t) = ______________ Answer(s) submitted: (incorrect) Find a vector function that represents the curve of intersection of the paraboloid z = 8x2 + 5y2 and the cylinder y = 2x2. Use the variable t for the parameter.

Explanation / Answer

3) P(-5,-2,-4), Q(-5,3,1)

equation of a line passing through 2 points

(x-x?) / (x?-x?) = (y-y?) / (y?-y?) = (z-z?) / (z?-z?)

(x-(-5)) /(-5-(-5)) = (y-(-2))/(-2-3) = (z-(-4))/(-4-1) = t

x+5/(-5+5) = t , y+2 / (-5) = t , z+4 /(-5) = t

x+5 = 0 , y+2 = -5t, z+4 = -5t

parametric equations are

x = -5, y = -5t-2,z = -5t - 4

vector equation of line

r(t) = (-5i-2j-4k) + ?(0i-5j-5k)

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