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)

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

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.