Question Parameterize the line through P = (3, 5) and Q = (13,7) so that the points P and Q correspond to the given parameter values. t = 0 and 5 (t) = [-14 Points] DETAILS HHCALCO 17.1.055. (a) Find a vector parallel to the line of intersection of the planes 3x - y - 4z = 0 and x + y + z = 1. (b) Show that the point (1,-1, 1) lies on both planes. To check that the point (1,-1, 1) lies on the planes, substitute it into each equation. 3x - y - 4z = 3.1- (-1) - 4.1 x + y + z = 1 - 1 + 1 Thus, the point lies on both planes. (c) Find parametric equations for the line of intersection. (Enter your answers as a comma-separated list of equations. Let x, y, and z be functions of t.)
UFOMIN The Asker · Calculus
Transcribed Image Text: Parameterize the line through P = (3, 5) and Q = (13,7) so that the points P and Q correspond to the given parameter values. t = 0 and 5 (t) = [-14 Points] DETAILS HHCALCO 17.1.055. (a) Find a vector parallel to the line of intersection of the planes 3x - y - 4z = 0 and x + y + z = 1. (b) Show that the point (1,-1, 1) lies on both planes. To check that the point (1,-1, 1) lies on the planes, substitute it into each equation. 3x - y - 4z = 3.1- (-1) - 4.1 x + y + z = 1 - 1 + 1 Thus, the point lies on both planes. (c) Find parametric equations for the line of intersection. (Enter your answers as a comma-separated list of equations. Let x, y, and z be functions of t.)
More Transcribed Image Text: Parameterize the line through P = (3, 5) and Q = (13,7) so that the points P and Q correspond to the given parameter values. t = 0 and 5 (t) = [-14 Points] DETAILS HHCALCO 17.1.055. (a) Find a vector parallel to the line of intersection of the planes 3x - y - 4z = 0 and x + y + z = 1. (b) Show that the point (1,-1, 1) lies on both planes. To check that the point (1,-1, 1) lies on the planes, substitute it into each equation. 3x - y - 4z = 3.1- (-1) - 4.1 x + y + z = 1 - 1 + 1 Thus, the point lies on both planes. (c) Find parametric equations for the line of intersection. (Enter your answers as a comma-separated list of equations. Let x, y, and z be functions of t.)
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Parametrization of a line isgamma(t)=u+tvwhere u is apoint on the line and v is a vector parallel to the limeGiven two points P=(3,5) and varphi=(13,7)If we want to parametrize the straight line passing through (3,5) and (13,7)we can take u=$(3,5)and v=(:3,5:)-(:13,7:)=(:-10,-2:)so parametrization of a line is{:[" can we write "gamma(t)=(:3","5:)+t(:-10","-2:)],[x(t)=3-10 t],[y(t)=5-2t]:}(a) pi_(1)quad3x-y-4z=0Comparing vec(gamma) vec(n)_(1)=dvec(n)_(1)≐3 hat(ı)- hat(ȷ)-4 hat(k)whichix normal vector at bar(A) । plare?{:[pi2quad x+y+z=1],[=>quad ... See the full answer