Purchase Solution

The equation of a plane

Not what you're looking for?

Ask Custom Question

Part I:

<(u x v), u> is greater than 0 for all vectors u and v in R^3.

Part II:

The equation of the plane through the origin determined by two vectors u and v in R^3 is <(u x v), x> = 0.

Are these statements true or false and please explain why.

Purchase this Solution
Solution Summary

This solution thoroughly demonstrates the equation of a plane.

Solution Preview

I. The statement is false. The cross-product u x v is perpendicular to both u and v, and so the dot product of (u x v) and u is zero for all u and v from R^3.

II. This statement is true. The equation of a plane can be derived as follows: ...

Purchase this Solution
Free BrainMass Quizzes
Probability Quiz

Some questions on probability

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

View More Free Quizzes
Related BrainMass Solutions

  • Calculus - Vectors - Vector Equation and Cartesian Equation

    A step by step solution is given in the attached file, explaining how to find the vector equation of a plane given three points and how to find the cartesian equation of the plane.

  • Equation for a plane

    Since (1,-1,3) is on it, we have 3*1+(-1)+3=A So, A=5 Hence, the equation of the plane is 3x+y+z=5 This shows how to find an equation for a plane. The parameters and parallel planes are determined.

  • plane equation

    Find the x, y, and z intercepts and sketch the plane. Please see the attachment. Write a plane equation for various contexts.

  • Equation of the tangent plane to the central conicoid

    16251 Equation of the tangent plane to the central conicoid Problem 1 Find the equation of the tangent plane to the central conicoid x2 - 4y2 + 3z2 + 2 = 0 at the point (1,2,0).

  • equation of a plane in 3-D space

    133358 Equation of plane Find the equation of a plane through the origin and perpendicular to: x-y+z=5 and 2x+y-2z=7 The normal vector of plane x - y +z = 5 is a = (1, -1, 1). The normal vector of plane 2x + y - 2z = 7 is b = (2, 1, -2).

  • Parametric equation of line and equation of plane

    So the parametric equation pasting through R and with above direction vector is The solution explains how to find the parametric equation of the line and the equation of a plane passing through three points in 3-D coordinates.

  • Cross Product : Finding the Equation of a Plane

    Then the normal vector of the plane is the cross product of the two vectors Then the normal vector can be So now we know the normal vector and the point O(0, 0,0), the plane equation is The equation of a plane is found.

  • Tangent Plane to Parametric Surface

    ., To find the equation of the tangent plane to the parametric surface at the point P , we need to find the normal vector of the tangent plane which is Hence, the equation of the tangent plane to the parametric

  • Equation of a plane

    Thus at we get: The plane equation is: Second method: The general equation of a plane is: This equation must satisfied by all points in the plane.

  • Find the equation of a tangent plane to a surface at a point.

    34297 Find the equation of a tangent plane to a surface at a point. Find the equation of the tangent plane to the surface z = e^(-2x/17) ln (3y) at the point...

View More Related Solutions