# Math - Equations of plane(check)

Consider the plane that contains points A(2,3,1), B(-11,1,2), C(-7,-3,-6).
a) Find two vectors that are parallel to the plane.
Ans: AC, BC or AB will be parallel to the plane.

b) Find two vectors that are perpendicular to the plane.
Ans: if i find the normal vector then i can use dot product and use arbitrary values to find the two vectors

c) Write a vector equation of the plane
Ans: I have two points AC, BC or AB and i have the normal, so i use them to write the vector equation.

d) Write the scalar equation of the plane.
Ans: the normal vectors are my coefficients for the(x,y,z) therefore if i substitute a point to find the constant 'd'

e) Write an equation of the line through the x- and y- intercepts of the plane
Ans: Find the x and y intercepts and those will be my points my z value being zero and using the normal as direction vector

Are the answers correct? I am a little confused, please correct if i am wrong somewhere.

1. 0
2. 0
3. 30
1. I actually did this problem
a) yes
b) the simplest normal is [1,-5,3) so any other multiple of that would do
c) [x,y,z] = [2,3,1] + s[13,2,-1] + t[9,6,7]
d) I got x - 5y + 3z = -10 , all 3 original points satisfied

e) for x-intercept, let both y and z = 0, so x=-10
for the point (-10,0,0)
for y-intercept let both x and z = 0, y = 2
for the point (0,2,0)
direction vector of line joining the intercepts is [10, 2,0] or [5,1,0]

so equation of line is [x,y,z] = 0,2,0) + t[5,1,0]

check my arithmetic, last time I made a silly error if you recall

1. 0
2. 0
posted by Reiny
2. for the e part of the question you mean:

[x,y,z]=[2,3,1]+t[10,2,0]+s[5,1,0]

right??

1. 0
2. 0
posted by Shaila

## Similar Questions

1. ### Math - Equations of plane(check)

Consider the plane that contains points A(2,3,1), B(-11,1,2), C(-7,-3,-6). a) Find two vectors that are parallel to the plane. Ans: AC, BC or AB will be parallel to the plane. b) Find two vectors that are perpendicular to the

asked by Shaila on September 4, 2010
2. ### calculus

I have 3 points: P(-3, 1, 2), Q(-1, 2, 3), R(2, 1, 0) and I need to find a nonzero vector orthogonal to the plane through these three points. I seem to recall this having something to do with the cross product, so I mad vectors PQ

asked by cross product on August 24, 2011

prove that normal to plane containing 3 points whose position vectors are a vector,b vector,c vectorlies in direction addition of cross product of vectors b and c and cross product of vectors c and a and cross product of vectors a

asked by parth on September 22, 2009
4. ### Physics

An air traffic controller observes two airplanes approaching the airport. The displacement from the control tower to plane 1 is given by the vector A , which has a magnitude of 220 km and points in a direction 32 degrees north of

asked by Hiral on June 28, 2012
5. ### Math

Suppose that a wind is blowing in the direction S45°E at a speed of 50 km/h. A pilot is steering a plane in the direction N60°E at an airspeed (speed in still air) of 150 km/h. The true course, or track, of the plane is the

asked by Matthew on September 14, 2015
6. ### Math

Me, again... Please help me. Thank you. Assume a plane is flying directly north at 200 mph, but there is a wind blowing west at 23 mph. Part I: Express both the velocity of the plane and the velocity of the wind as vectors, using

asked by Lizzie098 on January 9, 2014
7. ### Maths - Vectors

The position vectors a,b,c of the points A,B,C relative to the origin O are ai, bj and ck respectively.Find: 1) a vector equation for the line l throught O which is normal to the plane ABC. 2) a vector equation of the plane ABC

asked by Claire on February 2, 2009
8. ### Math - Vectors

Let the points A = (−1, −2, 0), B = (−2, 0, −1), C = (0, −1, −1) be the vertices of a triangle. (a) Write down the vectors u=AB (vector), v=BC(vector) and w=AC(vector) (b) Find a vector n that is orthogonal to both u

asked by Drake on May 31, 2016
9. ### Science

1) The vector sum of three vectors gives a resultant equal to zero. what can you say about the vectors? 2) Vector is 3.00 units in length and points along the positive x-axis. Vector is 4.00 units in length and points along the

asked by Sandy on November 19, 2009
10. ### Physics

1) The vector sum of three vectors gives a resultant equal to zero. what can you say about the vectors? 2) Vector is 3.00 units in length and points along the positive x-axis. Vector is 4.00 units in length and points along the

asked by Aman on November 19, 2009

More Similar Questions