The planes x + 2y + 3z = 12 and 2x + 3y + z equation is (x, y, z) = (0, 6, 0) + n(7, – 5, 1). Find the point in both planes for which: a) x = 7 = 18 intersect in the line l whose %3D b) y = 16

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: Determine whether the lines h and I, intersect, are parallel, or are skew. 1: n= 4i+3j+ (i-j+6k) 12:…

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Q: b) Obtain the equation of a plane, P that is orthogonal to the line L:x=1+4, y=8+1, z =9+9t_and goes…

A: Given line is                                       L1:x=1+4t, y=8+t, z=9+9tvector parallel to line…

Q: 1)calculate xy dxdy D where D is a parallelogram with vertices (0,0) ,(5,-1).(3, 1) and (8,0)

A: We have to evaluate the integral ∬ xy dxdy over D where D is a parallelogram. First we will sketch…

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: Q2. Find the equation of the line that passes through the point (-3,2,-1) and parallel to the line…

A: Given point is (-3,2,-1). And the planes are,

Q: Find the intersection of the line and plane: 3z (2x + y) = -5, P = ( r(t) = (3,-1,0) + t (-3, -2,…

A: Given line : r(t)= (3,-1,0)+t(-3,-2,-1) Given plane : 3z-(2x+y)=-5                       2x+y-3z-5=0…

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: Give an equation of the plane determined by the intersecting lines L1 and L2 = 2t 15 –t and L2 : {…

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Q: Using projection(s), find the distance between the point (0, −2) and the line 3x −2y + 5 = 0 (that…

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