Question

Find an equation for the line L that contains the point the point P = (−1, 3, 1) and is orthogonal to the line x − 2 /−1 = y − 1/ −2 = z − 5 /1 = λ, λ ∈ R

Answer #1

(a) Find the equation of the plane p containing the point
P(1,3,2)and normal to the line l which has parametric form
x=2,y=t+1,z=2 t+4.
Put x, y and z on the left hand side and the constant on the
right-hand side.
(b) Find the value of t where the line l intersects the plane
p.
(c) Enter the coordinates of the point where the line l
intersects the plane p.

Find the equation for the line through the point (2,0,2),
parallel to the plane x+y+z=10 and orthogonal to the line
r(t)=<1+t,1-t,2t>

Find an equation of the plane that passes through the point (-1,
-3, 1) and contains the line x = -1 - 2t, y = 4t. z = 2 + t.

Find the scalar equation for the plane passing through the point
P=(3, −5, −5) and containing the line L defined
by
x = 3+4t
y = −3−3t
z = −9+2t

Find the electric field at distance Y at point p above the
straight-line segment of Length L with linear charge density λ.
Point p is located at 1/3 L from the left of the line. Hint: in
this problem you need to find both X and Y components of the
electric field.

Find an equation of the plane.
The plane that passes through the point
(−1, 1, 3)
and contains the line of intersection of the planes
x + y − z = 4 and 4x − y + 5z = 5

find the parametric equation of the line passing through the
point (1,7,2), parallel to the plane x+y+z=2 and perpendicular to
the line x=2t, y=(3t+5)2, and z=(4t-1)/3

Find the electric field at distance Y at point
p above the straight-line segment of length L with
linear charge density λ. Point P is located at 1/3 L from the left
end of the line.
Hint: in this problem you need to find both X and Y
components of the electric field.

Find an equation of the plane. The plane that passes through the
point (?1, 1, 1) and contains the line of intersection of the
planes x + y ? z = 2 and 4x ? y + 5z = 3

Find an equation of the plane.
The plane that passes through the point
(−1, 1, 3)
and contains the line of intersection of the planes
x + y − z = 4 and 3x − y + 4z = 3

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