5. Determine the x-intercept of the plane: [x, y, z]= [3, 1, 3] + r[1, 1, − 1]+ t[0, 1, 3] ↑

Q: Find the linear equation of the plane through the point (2,3,6) and parallel to the plane…

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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: Find the point at which the line (-3, 3, 0) + t(-2, –3, –2) intersects the plane -2x – y + 3z = 5.

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Q: Determine the equation of the plane through the points (1, 0, 3) and the line l : ¯r = (3, 4, 1) +…

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Q: Find the point in which the line through P(3, 2, 1) normal to the plane 2x - y + 2z =-2 meets the…

A: Direction ratios of normal to plane 2x - y + 2z =-2  are <2,-1,2>, since line is normal to…

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 point at which the line (1, 2, 3) + t(5, 1, 1) intersects the plane -4x - 4y + 4z = -160.

A: Any point on the line <1, 2, 3> + t<5, 1, 1> can be expressed as         (1 + 5t, 2 + t,…