x(t) = 4+ t Find a plane through the point (-1,5,-3) and orthogonal to the line y(t) = 3 - 6t z(t) = 1 + 2t

Q: Find an equation of a plane containing the line r (-3, -3, -5)+t(4, 4, -2) which is parallel to the…

A: A plane containing the line r=-3, -3, -5+t4, 4, -2 which is parallel to the plane -2x+y-2z=8. We…

Q: Find the point(s) on x=3-y² that are closest the point A=(1,0)

A: Our Aim is to find the points on x=3-y2 that are closest the point A=(1,0).

Q: Find a plane containing the point (-5,-8,-7) and the line x (t) y(t) z(t) = = = −7+ 6t -3 - 2t - 2 +…

A: Given;

Q: Find the point at which the line (-3, 4, 2) +t(-4, 3, 1) intersects the plane -4x + y – 5z = 76.

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Q: (x(t) Find a plane containing the point (2,-4,-2) and the line y(t) z(t) = = = 2 - 5t 4 - 3t 5- 4t

A: Equation of the plane general form is  a(x-x_1)+b(y-y_1)+c(z-z_1)=0

Q: The temperature is T(x, y) = (x-1)² + y² degrees at any point (x, y) on a triangular metal plate…

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Q: Find a plane containing the point (-3,-3,5) and the line x(t) y(t) z(t) = = 8 + 4t -4-6t -7-3t

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Q: Find the distance from the point (0,1,-1) to the line a(t) = (-2, 2, 4)t + (-6, - 1,5)

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Q: Find an equation for the contour of f(x, y) = 2a²y + 6x + 15 that goes through the point (4, 1).…

A: A contour line of the quadric surface is the curve of intersection of the quadric surface with the…

Q: f(x) = xª -4 and Perpendicular to the line x - 4y + 1= 0.

A:

Q: Determine where the line y=6x +3 cuts y-axis A (-1,0) (-2,0) (+1,0) (-3,0) В (0,0) (0,–1) (0, +1) C…

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Q: Parameterize the line from (-1, 5) to (2, 3) so that the line is at (-1, 5) at t = 0, and at (2, 3)…

A: I am going to solve the problem by using some simple trigonometry to get the required result of the…

Q: If (x1, yı) and (x2, y2) are distinct points in the plane, show that y 1 1 =0 X1 x2 y2 is the…

A: If (x1, y1) and (x2, y2) are distinct points in the plane, to show that  xy1x1y11x2y21 =0 is the…

Q: Find the gradient of w= 3x² - 5y* + 2z at the point (1, 1, -2)

A: The given function is: w=3x2-5y2+2z2