An equation of the straight line normal to surface x2 - y3 + z = 8 at the point P(2, -1, 3) on the surface is given by : 4x - 3y + z = 14 4x -Зу + z%3D 8 4х + 5y - z%3D0 r (t) = (2 + 4t) i + (- 1 - 3t) j + (3 + t) k ,te r %3D r (t) = (- 2 + 4t) i + (1 - 3t) j + (-3 + t) k , te R %3D

Q: Suppose XY has coordinates X( -2, 5) and Y(3, -9). What are the coordinates for the midpoint of XY?

A: To find the Midpoint of the line.

Q: Find the Cross product of A= and B=

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Q: Q2/ Find the distance between the Line 2x - 2y + 1 = 0 & 3z + 2y = 4 to the Z-axis.

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Q: Perpendicular to y + x = 0; (2, 0) on line

A: To find equation of a line ,which is perpendicular to line y+x=0,and point (2,0) lies on line.…

Q: Parallel to x + 2y = 0; (1, 2) on line

A: To find the equation of line paralley to x+2y=0 and (1,2) is on the required line.

Q: find the y-intercept of the line that passes through (1,2,-3) and is parallel to the wing 1/3(x-4)=…

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Q: The lines y where = and y = MON 5x - 7 and y = 2x + 8 intersect at the point (x, y) N

A: To find the intersection of given lines.

Q: XIV. Give equation of straight line through point (1,3,-2) perpendicular to z = Зх-2y +4.

A: Given z=3x−2y+4 and point is x0,y0,z0=1,3,−2 We have to find the equation of straight line through…

Q: find equation for line parallel to y=4x-6 with y-intercept (0,3)

A:

Q: Find an equation for the contour of f(x, y) = 2a²y + 6x + 15 that goes through the point (4, 1).…

A: A contour line of the quadric surface is the curve of intersection of the quadric surface with the…

Q: Find the equation of the line perpendicular to the lines x-1 x+1 쯤 and 1 and 2 == 2-1 2 2 4 3 = y-1…

A: (x-1)/2 = (y-1)/2 = (z-3)/2  And (x+1)/4 =y/3 =(z-1).

Q: Find the points of intersection of x = 4y and y = 4x. (ans.:(0,0),(16,64))

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Q: Find the parametric and symmetric equations for the line passing through the point P(1,-3,6) and it…

A: Equation of the line passing through the one  point and parallel to the given line

Q: i 6i + 2j+ 2k + 2(i- 2j+2k) Find the shortest distance between lines -4i -i + 4(3i - 2)- 2k) and

A: The given lines are as follows- r→=6i^+2j^+λi^-2j^+2k^          ........(1)r→=-4i^-k^+μ3i^-2j^-2k^…