Let L be the line passing through the point P(1, 2, -1) with direction vector d=[-2, -3, -4]", and let T be the plane defined by -3x+5y-2z=-17. Find the point Q where L and T' intersect Q=(0, 0, 0)

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 equation of the plane that X-3 contains the lines =y= z+1 4 and X+2= =y-5= 2 Z-3 4 2 -16x -…

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Q: Let L. be the line passing through the point P=(5, 1, 1) with direction vector [-1,5, -2], and let T…

A: Solution :

Q: 9 Find the distance from the point (-7,-3,4) to the xy-plane.

A: Distance of a point (a,b,c) from the plane lx+my+nz=p is (la+mb+nc-p)/sqrt(l^2+m^2+n^2)

Q: Compute the distance between the point (-2, 8, 1) and the line of intersection between the two…

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Q: Find the distance from the point Q = (1, -3, 3) to the plane 2x + 2y + 5z = 2.

A: The equation of the plane is 2x+2y+5z=2Here we have to find the distance between the plane and the…

Q: Let Lz be the line passing through the point P-(10, 1. –10) with direction vector d--2, -2, 3]", and…

A: We will use formula for the shortest distance.

Q: Determine the point at which the line passing through the points P(1, 0, 6) and Q(7, -1, 7)…

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Q: Find the point of intersection of the line with equation L: (x,y,z) = (1, - 1,0) + t(1,1,2) and the…

A: To find the intersecting point, we substitute the values of x, y, and z in the equation of plane and…