Question

Vector v is shown in the graph.

vector v with initial point at 0 comma 0 and terminal point at negative 5 comma 12

What are the component form and magnitude of v?

Answer 1

366

Explanation:

To calculate the dot product of vectors u and v, we need to find the product of their corresponding components and then sum them up. The dot product formula is given by:

u · v = u_x * v_x + u_y * v_y

where u_x and u_y are the x and y components of vector u, and v_x and v_y are the x and y components of vector v.

Let's find the components of vectors u and v first:

u = (-6, -10)

v = (7, 8)

Now we can calculate the dot product:

u · v = (-6 * 7) + (-10 * 8)

= -42 - 80

= -122

Finally, to find -3(u · v), we multiply the dot product by -3:

-3(u · v) = -3 * (-122)

= 366

Therefore, -3(u · v) is equal to 366