Finding the Nonzero Vector and Area of Triangle

In summary, to find a nonzero vector orthogonal to the plane through points P, Q, and R, use the cross product of vectors PQ and PR. The length of the cross product is equal to half of the area of the triangle PQR.
  • #1
Physicsnoob90
51
0

Homework Statement



Find a nonzero vector orthogonal to the plane through the point P, Q,and R. (b) also find the area of triangle PQR

P(1,0,1) , Q(-2,1,3) , R(4,2,5)

Homework Equations


-Cross product
-Finding the Angle
-Area formula

The Attempt at a Solution



My steps:
1. i found the vectors for PQ = <-3,1,2> and PR = <3,2,4>

2. i perform the cross product (PQ X PR), which got me <0,18,-9>

Can anyone help me?
 
Physics news on Phys.org
  • #2
NVM, i just solved it!
 
  • #3
It is a basic property of the cross product that the length of the cross product of vectors u and v is the area of the parallelogram having vectors u and v as to adjacent sides and so 1/2 the length of their cross product is the area of the triangle having u and v as sides.
 

FAQ: Finding the Nonzero Vector and Area of Triangle

What is a nonzero vector?

A nonzero vector is a vector that has a magnitude (length) and direction, and is not equal to the zero vector (a vector with a magnitude of 0).

How do you find the nonzero vector of a triangle?

To find the nonzero vector of a triangle, you can use the cross product or vector product of two of its sides. This will give you a vector that is perpendicular to both sides and has a magnitude equal to the area of the triangle.

What is the formula for finding the area of a triangle?

The formula for finding the area of a triangle is A = 1/2 * b * h, where b is the base of the triangle and h is the height. Alternatively, you can also use Heron's formula, which takes into account all three sides of the triangle: A = √(s(s-a)(s-b)(s-c)), where s is the semiperimeter (half of the perimeter) and a, b, and c are the lengths of the sides.

How do you find the area of a triangle using vectors?

To find the area of a triangle using vectors, you can use the magnitude of the cross product or vector product of two of its sides. This will give you the area of the parallelogram formed by those two sides, and since a triangle is half of a parallelogram, you can divide the result by 2 to get the area of the triangle.

Can the nonzero vector and area of a triangle be negative?

Yes, it is possible for the nonzero vector and area of a triangle to be negative. This would occur if the orientation of the triangle is reversed or if the angle between the two sides used to find the vector or area is greater than 180 degrees.

Similar threads

Finding an area of a triangle formed by three points
Replies
2
Views
2K
Area of a triangle using vectors
Replies
3
Views
2K
Prove area of triangle is given by cross products of the vertex vectors....
Replies
6
Views
8K
Finding an Orthogonal Vector and Calculating Triangle Area from Given Points
Replies
2
Views
6K
Unit vector orthogonal to plane
Replies
2
Views
6K
Finding the scalar equation of a plane
Replies
2
Views
2K
Unit Vector Perpendicular to a Triangle?
Replies
3
Views
9K
Inner Product, Triangle and Cauchy Schwarz Inequalities
Replies
5
Views
3K
Finding maximal area of triangle.
Replies
3
Views
2K
Question about determining the angles of triangle given two vectors
Replies
3
Views
4K

Hot Threads

Recent Insights

Back
Top