Q3A) Find normal line and parallel plane to the function f(x, y, z) = x²y²z² - 4 At point (1,-1,2).

Q: Parameterize the line connecting the points P = (1, 1, 2) and Q = (-2,0,3).

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Q: BA)Find normal line and parallel plane to the function f(x, y, z)=x√yz + 6 At point (-3,1,4).

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

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Q: The slope of the curve 2x + Vx + y = y at the point (0, 1) is

A: 2x + √(x+y) = y  So,  √(x+y) = y - 2x So, x+y = (y-2x)² So, x+y = y² + 4x² - 4xy  So, y(1+4x) - y² =…

Q: Find Vƒ(P) and D7f(P). (a) f(r, y, 2) = yf + z² – 4xz; Ū = } i – $ j+ k; P(-2,1,3)

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Q: Find the distance of the point (1,3) from the line 2x-3y+9=0 measured along a line x-y+1=0.

A: Firstly we will find a line passing through (1,3) and parallel to x-y+1=0 Then the point of…

Q: Find the distance from the point (0,1,-1) to the line a(t) = (-2, 2, 4)t + (-6, - 1,5)

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Q: Find the distance from the point (2, 2, 3) to the line x = 0, y = 2+2t, z = 3+ t.

A: Find the distance from the point (2, 2, 3) to the line x= 0, y=2+2t, z=3+t.

Q: Find the distance from the point (2, 2, 3) to the line x = 0, y = 2 + 2t, z = 3 + t.

A: Given point (2,2,3)and line is x=0 , y=2+2t ,z=3+t.

Q: Find point P(x,y) if it is equidistant between points A(2,9) and B(-3,6)

A: Given:-  Px,y is equidistant  from the points  A2,9  and  B -3,6 i.e,  AP=BP and  we know  that…

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

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Q: Calculate the distance between the points S=(-3,-7) and M=(2,-1)

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Q: Find the distance between the line x + y + 2 = 0 and the point (1, 1).

A: The distance between the line ax+by+c=0 and the point x1,y1 is given as below. d=ax1+by1+ca2+b2

Q: Find the distance from the point (-3,0,-7) to the line a(t)=t +

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