Question

How do we find the orthogonal projection of Y onto the basis

( -4 ) (1) ( -2 )
let y = ( -8 ) u₁ = (-2) u ₂ = ( 2 )
( 5 ) (-1 ) ( -6 )
Compute the dot product between u₁ and u₂

Answer 1

To compute the dot product of vectors u1 and u2, you multiply their corresponding components and add them together. For u1 = (-4, 1, -2) and u2 = (-2, 2, -6), the dot product is 22.

Step-by-step explanation:

To compute the dot product between vectors u1 and u2, we multiply corresponding components of the vectors and then sum the products. The vectors given are u1 = (-4, 1, -2) and u2 = (-2, 2, -6).

The dot product u1 ⋅ u2 is calculated as follows:

• u1 ⋅ u2 = (-4)(−2) + (1)(2) + (-2)(−6)
• u1 ⋅ u2 = 8 + 2 + 12
• u1 ⋅ u2 = 22

So the dot product of u1 and u2 is 22, which is a scalar quantity.