Question

Examine whether or not these pair of lines are perpendicular to each other. (1) y - 3x - 2 = 0 and 3y + x + 9 = 0 (2) 3y - 4 = 2x + 3 and y-5 = x+ 6 (3) Find the equations of the tangent and normal to the curve xsquare + ysquare+3xy-11 = 0 at the point x = 1, y = 2.

Answer #1

1. Determine whether the lines are parallel, perpendicular or
neither. (x-1)/2 = (y+2)/5 = (z-3)/4 and (x-2)/4 = (y-1)/3 =
(z-2)/6
2. A) Find the line intersection of vector planes given by the
equations -2x+3y-z+4=0 and 3x-2y+z=-2
B) Given U = <2, -3, 4> and V= <-1, 3, -2> Find a. U
. V b. U x V

Find equations of the tangent lines to the curve f (x) = (2x
+1)/(4x-3) that are perpendicular to the line 5x−2y+2=0.
Explanation would be appreciated!

The equations of three lines are given below Line 1: y=3x-5 Line
2: y=-1/3x +1 Line 3: 3x-9y=18 For each pair of lines, determine
whether they are parallel, perpendicular, or neither: 1. Line 1 and
2 are they (parallel, perpendicular, or neither.) 2. Line 1 and 3
are they (parallel, perpendicular, or neither.) 3. Line 2 and 3 are
they (parallel, perpendicular, or neither.

Find the equations of the tangent and normal to the curve
x2 + y2+3xy-11 = 0 at the point x = 1, y =
2.

at
what point on the curve y=sqrt(1+2x) is the tangent line
perpendicular to the line 15x+3y=1

1. Solve all three:
a. Determine whether the plane 2x + y + 3z – 6 = 0 passes
through the points (3,6,-2) and (-1,5,-1)
b. Find the equation of the plane that passes through the points
(2,2,1) and (-1,1,-1) and is perpendicular to the plane 2x - 3y + z
= 3.
c. Determine whether the planes are parallel, orthogonal, or
neither. If they are neither parallel nor orthogonal, find the
angle of intersection:
3x + y - 4z...

What are the equations of the tangent and normal lines to the
following curve: y2+y+x =
arctan2(sin3(x)) at point (0,-1) Remember
that (arctan (u)=tan-1(u))

Find equations of the tangent lines to the curve y = x − 1/x + 1
that are parallel to the line x − 2y = 3. y= y=

Find equations of all lines having slope negative 1 that are
tangent to the curve y equals 1/x+9

Sketch the curve y = x^2 + 5 , and the point (0,-6) on the
same
coordinates. Find the equations of the lines that pass through the
point
(0,-6) and tangent to the curve y = x^2 +5 at the point x = a.
(Hint there
are two values of a : a > 0 and a < 0 )

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