Given Bold u equals negative Bold i plus Bold j , Bold v equals 10 Bold i minus 2 Bold j , and Bold w equals negative 8 Bold j , find proj Bold Subscript u left parenthesis Bold v plus Bold w right parenthesis.

Given u=-i+j, v=10i-2j, and w = -8j

find proj Subscript u (v+w)

Answer: u. (v+w) = - 20

Step-by-step explanation:

Given;

u = - i+j

v = 10i-2j

w = - 8j

v+w = 10i-2j + (-8j)

v+w = 10i-10j

u. (v+w) = (-i+j). (10i-10j)

= - 1*10 + 1 * -10

= - 10-10

u. (v+w) = - 20

Answer: u (v+w) = - 20

Step-by-step explanation: u, v and w are vectors in the x-y plane, where i is related to the x-axis and j is related to the y-axis. Vectors can be added, subtracted or "perform" an operation called dot product.

In this question, we have: u. (v + w)

To resolve it, first add the vectors:

(v + w) = (10i - 2j) + (-8j)

(v + w) = (10i - 10j)

Now, the dot product:

u. (v + w) = (-i + j). (10i - 10j)

u. (v + w) = (-1) (10) + (1). (-10)

u. (v + w) = - 10 - 10

u. (v + w) = - 20

Note that the sum of vector gave another vector. However, the dot product of vectors produce a scalar because it's the sum of the product of the horizontal elements with the sum of the product of the vertical elements.