Determine the point of intersection, if such a point exists, for the line €: (x, y, z) = (3,– 1, 7) + r(-5, 2, 1) and the plane 2x + 3y + 4z = 24.

Q: Determine the geometric location of the points in R3 that equidistant from the plane y = 3 and the…

A: This is question of 3d geometry and locus.

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

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Q: Represent two planes that intersect at a line represented by 3. y- 7 = z+2 2.

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Q: by the equations { L₁ : X Y Let L₁ and L2 be lines in a 3-dimensional space given { = = Z = 3 + 2t…

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Q: 2. Write the symmetric equation of a line through the points (0, 2,8) and (3,-3, 4). Find where this…

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Q: Find an equation for the plane through P(1,4,4) that contains the line of intersection of the planes…

A: Let the equation of the plane that contains the line of intersection of the planes 3x-y+3z=-1 and…

Q: This table gives a few (, y) pairs of a line in the coordinate plane. -38 40 -23 30 -8 20 What is…

A: To find the x-intercept first we have to find the equation of line that passes through these point…

Q: Determine if the line given by r(t)=(-2t, 2+7t, -1-4t) intersects the plane given by 4x+9y-2z =-8…

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Q: Find the equation of the plane that contains the line r¡(t) = (1 + lt, –1+t, 2+ 8t) and the point…

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Q: ind the line of intersection of the planes x+y+z=1 and y+z=0

A: The given planes are x+y+z=1 and y+z=0. It is required to find the equation of line of intersection.…

Q: Find the intersection point(s) (if any) of the line r(t) = (21,-14, -9) + t(2,3,4) and the plane 19…

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Q: Find the equation of the plane that passes through (3,4,-1) and contains the line of intersection of…

A: To work out the equation of the required plane satisfying the given geometric conditions