Question

In: Advanced Math

a. Find the x-perpendicular of the projection of (1,1,1,1,1) onto (1,2,3,4,1). b. What is the projection...

a. Find the x-perpendicular of the projection of (1,1,1,1,1) onto (1,2,3,4,1).

b. What is the projection of the projection of (1,1,1,1,1) onto (1,2,3,4,1)? Make a sketch.

Expert Solution

Given two vectors and , we can resolve the vector into two components i.e. one component in the direction of and another component in the perpendicular direction of .

The component in the direction of is given by the projection of onto i.e.

The component perpendicular to is given by

Hence

Now, in order to find the x-perpendicular of the projection, we need to find the projection and the perpendicular component of . Therefore, let's resolve part(b) first.

b)

Using the above formula

Hence,

a)

From the above formula we have

Hence, x-perpendicular of the projection (1,1,1,1,1) onto (1,2,3,4,1) is

Colby Messinger answered 1 month ago

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