Question

Let u = (3,-2) and v = (-2,5). find the (a) component form and (b) magnitude (length) of the vector.

Answer 1

The component form of vector u is (3, -2), and its magnitude is √13. The component form of vector v is (-2, 5), and its magnitude is √29.

Step-by-step explanation:

To find the component form and magnitude of the vector given by u = (3,-2) and v = (-2,5), we first need to understand that the component form of a vector is simply the vector itself, which is expressed as an ordered pair (x, y) in two-dimensional space. Hence, for vector u, the component form is (3, -2), and for vector v, the component form is (-2, 5).

The magnitude (or length) of a vector w = (x, y) can be found using the formula
`|w| = sqrt(x^2 + y^2)`. Therefore, the magnitude of vector u is
`|u| = sqrt(3² + (-2)²) = sqrt(9 + 4) = sqrt(13)`, and the magnitude of vector v is
`|v| = sqrt((-2)^2 + 5^2) = sqrt(4 + 25) = sqrt(29).`