Question

The component forms of vectors u andv are given by u =(5,3) and v = (2,-7).Given that 2u+(-3v)+w=0, what is thecomponent form of w?

Answer 1

To find the component form of vector w, we'll use the given equation: 2u + (-3v) + w = 0. Plugging in the values of u and v, we can solve for w and find its component form as (-4,-27).

Step-by-step explanation:

To find the component form of vector w, we'll use the given equation: 2u + (-3v) + w = 0. We already know the component forms of vectors u and v, which are u = (5,3) and v = (2,-7) respectively.

Substituting these values into the equation, we can solve for w. Rearranging the equation, we have w = -2u + 3v.

Plugging in the values, we get w = (-2*5, -2*3) + (3*2, 3*(-7)), which simplifies to w = (-10, -6) + (6, -21). Adding these vectors together, we get w = (-4,-27).