# Calculus and vectors

posted by .

A plane, π, has 3x-5z+3=0 as its Cartesian equation. Determine the Cartesian equation of a plane that is perpendicular to π and contains the point P(2,9,-3)

• Calculus and vectors -

the normal of the given plane is
(3,0,-5) which is then the direction of your line

A vector equation of that line is
r = (x,y,z) = (2,9,-3) + t(3,0,-5) where t is your parameter

x = 2 + 3t ---> t = (x-2)/3
y = 9 + 0t ---> y = 9
z = -3 - 5t --> t = (z+3)/-5

so

(x-2)/3 = (z+3)/-5 , y = 9

## Similar Questions

1. ### Math

This question makes reference to an orthonormal basis (i,j), and an origin O. 1. Consider the triangle ABC, with vertices A(0,-2), B(9,1), C(-1,11). Find: a) a cartesian equation of the altitude from C; b) a cartesian equation of the …
2. ### Vector

2. Determine the Cartesian equation of the plane passing through the point P(2, -1,2) and containing the line r = (2, -1, 4) + f(0, 3, -5).
3. ### vectors

What is the cartesian equation of the xz plane
4. ### Math1239

x=4 cost, y= 2 sint on the interval 0 ≤ t ≤ 2π what is the Cartesian equation?
5. ### vectors HELP!

determine an equation of the plane that is perpendicular to the plane x+2y+4=0, contains the origin, and has a normal that makes an angel of 30 degrees with the z-axis.

Which of the following are trigonometric identities?
7. ### calculus

A) Determine the vector equation of the plane that contains the following two lines: l1: vector r= [4,-3,5] + t[2,0,3], tER l2: vector r= [4,-3,5] + s[5,1,-1], sER b)Determine the corresponding Cartesian equation.
8. ### Calculus

For the question "Determine the equation of the tangent to the curve y = xtanx at the point with x-coordinate π." how is the answer -πx + y + π2 = 0?
9. ### Cartesian Equation

Determine the Cartesian equation of each of the following planes: b) through the points (3,0,1) and (o,1,-1), and perpendicular to the plane with equation x-y-z+1=0 My teacher told me to find a direction vector, cross that with the …
10. ### vector calculus

Hi, I'm having trouble answering this question. The lines l1 and l2 are defined as l1: (x-1)/3 = (y-5)/2 = (z-12)/-2 l2: (x-1)/8 = (y-5)/11 = (z-12)/6 The plane j contains both l1 and l2. Find the Cartesian equation of j.

More Similar Questions