Write the given vector as the product of its magnitude and a unit vector. (Write the unit vector so that it is in the same direction as the given vector. This means that the signs of the components of the unit vector should be the same as the signs of the corresponding components of the given vector.)

Question

Quizplus · Accepted Answer

To find the unit vector, we need to divide the given vector by its magnitude. The magnitude is the square root of the sum of the squares of its components, which is sqrt((11^2) + (0.2^2) + (-6^2) + (3^2)) = sqrt(146.04) = 12.08 (rounded to two decimal places). Dividing the given vector by its magnitude, we get (11/12.08, 0.2/12.08, -6/12.08, 3/12.08) = (0.9107, 0.0166, -0.4967, 0.2484). Therefore, the product of the magnitude (12.08) and the unit vector (0.9107, 0.0166, -0.4967, 0.2484) is equal to the given vector (11, 0.2, -6, 3). The closest answer choice is C, with the same first four components as the unit vector we found.

Write the Given Vector as the Product of Its Magnitude