Let L. be the line passing through the point P-(4, -3, 1) with direction vector a-[-4, 1, 1], and let T be the plane defined by 5x+4y-4z=37. 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: Let A be the point with coordinates (1, 9, 5), let B be the point with coordinates (-3, 5, 1), let C…

A: Given coordinates are, A=1,9,5B=-3,5,1 So, the midpoints of AB is C1-32,9+52,5+12=C-1,7,3.

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: nterseeting Lines Finad the plane determined by the Loi Xi=l-2t, , J="l-st,, 2= -2+t, L2: X2=-3+t2,…

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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: Q3// :- Write an equation for the plane containing points P=(1,1,-2),Q=(0,2,1), and R=(-1,-1,0)

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Q: Let / denote the line in R with equation y = = 3x - 2. Let Q = (2, -1). (a) Write the line / in…

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