Question

The orthogonal projection of a¯=2i+3j+3k on b¯=i−2j+k is

Answer 1

Given: a(bar) =2i + 3j + 3k on b(bar) = i − 2j + k

To find: Orthogonal projection of a on b?

Solution:

• Orthogonal projection: It is a two-dimensional graphic representation of an object in which the projecting lines are at right angles to the plane of the projection.

• Now we know the formula for orthogonal projection, that is:

• Orthogonal projection of a on b = a.b / mod(b)² x b(vector)

                 ( 2i + 3j + 3k . i − 2j + k / 1+4+1 ) x   i − 2j + k

                 ( 2 - 6 + 3 / 6 ) x  i − 2j + k

                 -1/6 x  i − 2j + k

                 -i +2j -k / 6

Answer:

            Orthogonal projection of a on b is -i +2j -k / 6