Question

Let u = 5(i) -(j) , v = 3(i) +(j), and w =(i) + 7(j) . Find the specified scalar uv+uw. (Simplify your answer.)

a. 2i+6j
b. -2i-6j
c. 2i−6j
d. −2i+6j

Answer 1

To find the specified scalar uv+uw, the dot products of vectors u with v and u with w are calculated and added. The result is 12.

Step-by-step explanation:

To find uv+uw, you need to perform vector multiplication and addition. First, calculate the dot product of vectors u and v, then the dot product of vectors u and w. After that, you can add the two results.

Let's define the vectors as follows:

u = 5i - j
v = 3i + j
w = i + 7j

The scalar dot product uv is given by (5i - j) · (3i + j) = 15i·i + 5i·j - 3j·i - j·j = 15 - 1 = 14, since i·i = 1, j·j = 1, and i·j = j·i = 0.

Next, calculate the dot product uw: (5i - j) · (i + 7j) = 5i·i + 35i·j - j·i - 7j·j = 5 - 7 = -2.

Now, add the two scalar products: uv + uw = 14 + (-2) = 12.