Friday

October 24, 2014

October 24, 2014

Posted by **Shaila** on Tuesday, August 10, 2010 at 3:39am.

What is actually meant by mutually orthogonal?

- Math - Vectors -
**jai**, Tuesday, August 10, 2010 at 11:25pmmutually orthogonal=the three of them are orthogonal (or perpendicular) to each other,, [angle between them is 90 degrees]

first recall the formula for the dot product. for any given vectors A and B,

A(dot)B=|A||B|cos(theta)

where |A| and |B| are the magnitude of vectors A and B respectively

*note: magnitude means you get the squareroot of the sum of the squares of each element in the given vector.

example, the vector <1,-2,4> has a magnitude of squareroot of (1^2+(-2)^2+4^2) or squareroot of 21

*note: A(dot)B is the sum of the products of the respective elements (x, y and z elements) of two given vectors [this is scalar]

example, A<2,-1,3> and B<-3, 2, 0>

A(dot)B = 2*-3 + -1*2 + 3*0 = -8

going back to your question,

i<1,0,0> ; |i|=1

j<0,1,0> ; |j|=1

k<0,0,1> ; |k|=1

note that i(dot)j is zero, as well as i(dot)k and j(dot)k,,

therefore in the equation, A(dot)B=|A||B|cos(theta)

cos(theta) is equal to zero (since 0/1=0)

therefore, theta you will get is 90 degrees (for i(dot)j, i(dot)k and j(dot)k), which means they are mutually orthogonal to each other,,

so there,, i'm sorry for long explanation..

**Answer this Question**

**Related Questions**

Mamthematics - Vectors - a) If vector u and vector v are non-collinear vectors ...

Math - Mark each of the following True or False. ___ a. All vectors in an ...

math - given that vectors(p+2q) and (5p-4q) are orthogonal,if vectors p and q ...

Math - I'm doing a bunch of practice finals and I don't know how to approach ...

math - Prove that if A is a symmetric n x n matrix, then A has a set of n ...

math - Can I please get my answers double checked? True or False 1. The tangent ...

math - Find the least squares approximation of x over the interval [0,1] by a ...

math - A trigonmetric polynomial of order n is t(x) = c0 + c1 * cos x + c2 * cos...

math - Find an orthonormal basis for the subspace of R^3 consisting of all ...

TRIGONOMETRY - Use the dot product to determine which of the following vector ...