Determine whether the line and plane intersect; if so, find the coordinates of the intersection. (a) x=t, yt, z = t 3x - 2y + z-5=0 The line and the plane Choose one (b) x = 2-t, y = −2+t, z = t 6x +9y5z -4 = 0 The line and the plane Choose one Choose one intersect do not intersect

Q: Find the point, P, at which the line intersects the plane. x= - 3+ 10t, y = 9- 9t, z= 9- 7t; - 10x +…

A: The objective is to find the point of P, at which the line intersects the plane.

Q: Find an equation for the plane through the point (0, –4, 5) which is perpendicular to the line…

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Q: In the diagram given below, the equation y 3. %3D x+3 represents the surface of a mirror. A ray of…

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Q: (x = t r:{y = -t (z = 1+ 4t concurrent, and if so, determine the point P common to them. Check if…

A: Let the equation of a line passes through the point x0,y0,z0 with the direction vector v→=l,m,n be…

Q: b0 = -6, b1 = 5, b2 = 0a. determine whether the plane slopes upward, slopes downward, or is…

A: (a)Direction of the slope of a plane:If the sign of a partial slope is positive, the plane slopes…

Q: Can the x-intercept and the y-intercept of a line be the same point? Explain. O Yes, when the line…

A: Given

Q: Find the points on the coordinate plane 2,3) and Q(2.-2.-1)

A: Given query is to find point P and Q on coordinate plane.

Q: Write an equation for a) the line through (2, 3) and (- 3, 6). b) the line through (-2, - 1) and…

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Q: Q4-Find the Cartesian equation of the line that passes through the point (-3, 2,-1) and is parallel…

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Q: Points A(p, 6), B(-3, q), and C(r, 8) are on a line whose equation is y = -2x + 3. Find the unknown…

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Q: b0 = 6, b1 = -2, b2 = -1a. determine whether the plane slopes upward, slopes downward, or is…

A: a)Direction of the slope of a plane:If the sign of a partial slope is positive, the plane slopes…

Q: Determine the point where the lines x = 4t + 1, y = t - 9, z = 2t + 1 and x = 5s + 1, y = -s, z = 5s…

A: The given lines are:L1:    x=4t+1,   y=t-9,   z=2t+1L2:    x=5s+1,  y=-s,    z=5s-9

Q: Explain why the equation 7 = (-1,0, -1) + s(2,3,-4) + t(4,6,-8) where s, t ER does not represent the…

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Q: x², if x 2 and x 36 5. q(x) · 10 – x,

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Q: Find an equation of the plane. The plane that passes through  (7, 0, −2)  and contains the line  x…

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Q: Find the equation of perpendicular bisector of the line s oining the pointsA(2, 3) and B(6, −5).

A: Provided that    A=(x,y)=(2,3) and B=(x',y')=(6,-5). The slope of AB is given by s, which can be…

Q: Find an equation of the plane that contains the two parallel lines and x −1 y + 1 3 2 x + 3 y 4 3 2…

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Q: In the Cartesian plane below, the map of two perpendicular cross country skiing trails is shown that…

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Q: b0 = -2, b1 = 3, b2 = -7a. determine whether the plane slopes upward, slopes downward, or is…

A: (a)Direction of the slope of a plane:If the sign of a partial slope is positive, the plane slopes…

Q: Which of the following equations represents a line perpendicular to y = 2x – 7 and passing through…

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