Find out a vector that is orthogonal to the plane, Mathematics

Assignment Help:

A plane is illustrated by any three points that are in the plane.  If a plane consists of the points P = (1, 0,0) , Q = (1,1,1) and R = (2, -1, 3) find out a vector that is orthogonal to the plane.

Solution

The one way which we know to get an orthogonal vector is to take a cross product. Thus, if we could find two vectors which we knew were in the plane and took the cross product of these two vectors we know that the cross product would be orthogonal to both of the vectors.  Though, as both the vectors are in the plane the cross product would then as well be orthogonal to the plane.

Thus, we require two vectors that are in the plane. This is in which the points come into the problem. As all three points lie in the plane any vector among them must as well be in the plane. There are several ways to get two vectors in between these points.  We will make use of the following two,

2475_Find Out a Vector that is Orthogonal to the Plane 2.png

The cross product of these types of two vectors will be orthogonal to the plane. Thus, let's find the cross product.

609_Find Out a Vector that is Orthogonal to the Plane.png

Thus, the vector 4i + j - k will be orthogonal to the plane consisting of the three points.


Related Discussions:- Find out a vector that is orthogonal to the plane

Trig, I need help with this question: Find the probability that two quarter...

I need help with this question: Find the probability that two quarters and a nickel are chosen without replacement from a bag of 8 quarters and 12 nickles.

Example of subtraction , Example of subtraction: Example: Subtrac...

Example of subtraction: Example: Subtract 78 from 136. Solution:     2 136 -78 ------  58 While subtracting the units column, 6 - 8, a 10 that is b

Logarithmic function:solve for x: 4 log x2, Solve for x: 4 log x = log (15 ...

Solve for x: 4 log x = log (15 x 2 + 16) Solution:              x 4 - 15 x 2 - 16 = 0                (x 2 + 1)(x 2 - 16) = 0                x = ± 4   But log x is

Applied Math, Calucations of gradients find f Graph some level curve f=cons...

Calucations of gradients find f Graph some level curve f=const. f=9x^2 = 4y^2

Determine probability , You are going on a road trip and you buy snack pack...

You are going on a road trip and you buy snack packs and three different kind of beverages.  You buy 7 Cokes, 5 Pepsis and 4 Dr. Peppers.  You pull out two beverages at random.  An

Determine the approximate raw act score, Using the same mean and standard d...

Using the same mean and standard deviation as mean m = 20.1 and a standard deviation s = 5.8. Joe was informed that he scored at the 68 th percentile on the ACT, what was Joe's ap

I NEED HELP WITH A MATH PROJECT., HOW MUCH WILL A NEW CAR COST? THE AVERAGE...

HOW MUCH WILL A NEW CAR COST? THE AVERAGE COST OF A NEW CAR IN 1990 WAS $14371. IN 2003 THE AVERAGE COST HAD RISEN TO $22360. WHAT IS THE AMOUNT OF THE MONTHLY PAYMENT? THE AMOUNT

Matrices, find inverse of [1 2 3 2 4 5 3 5 6]

find inverse of [1 2 3 2 4 5 3 5 6]

Obtain the equation of the diagonals, the sides of a quad  taken at random ...

the sides of a quad  taken at random are     x+3y-7=0              x-2y-5=0 3x+2y-7=0               7x-y+17=0  obtain the equation of the diagonals

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd