mutually 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..
Prove that vector i,j and k are mutually orthogonal using the dot product.
What is actually meant by mutually orthogonal?
1 answer