Question

find any vectors which are orthogonal to the vector <2,5,-3>

Answer 1

Any vector (x,y,z) which are orthogonal to the vector <2,5,-3>, their dot product is 0.

Thus, we get:

2x + 5y - 3z = 0

So,

.

Thus, Any vector (x,y,z) which are orthogonal to the vector <2,5,-3> is given by:

where x and y can take any value.

For example, putting y = 1, y = 1:

the vector

i.e.,

< - 1, 1, 1> is orthogonal to the vector <2,5,-3>

because the dot product:

(-1) X 2   + 1 X 5   + 1 X (-3)

= - 2 + 5 - 3 = 0