Let L be the line passing through the point P=(4, -3, 1) with direction vector -[-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: 2. Find an equation (parametric and vector form) of the line if the line is perpendicular to the…

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Q: Find an equation of a plane containing the line r (-3, -3, -5)+t(4, 4, -2) which is parallel to the…

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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: Find the distance from the point P(1, 4, 0) to the plane through A(0, 0, 0), B(2, 0, -1), and C(2,…

A: Given points A0,0,0 , B2,0,-1 & C2,-1,0The direction ratios of AB⇒2-0,0-0,-1-0=2,0,-1Similarly…

Q: Find a scalar equation of the plane containing the line and the point (-5, -1,5). x = 6 +8t, y=-1-3t…

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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: 2. Find the equation of the planes: a) (in general form) that goes through the three points A(4, 0,…

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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: Let L. be the line passing through the point P-(4, -3, 1) with direction vector a-[-4, 1, 1], and…

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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: 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: 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 distance between (1,-2, - 1)and the plane through the points (1, 2, 3)and (3 , 2, 1)and…

A: Given information: The plane passes through the points (1, 2, 3) and (3 , 2, 1) and perpendicular to…

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…