Question

Find a unit vector that has the same direction as the given vector. −3i 7j

Answer 1

To find a unit vector with the same direction, divide the given vector by its magnitude and simplify.

Step-by-step explanation:

To find a unit vector that has the same direction as the given vector -3i + 7j, we need to divide the given vector by its magnitude. The magnitude of a vector is found using the formula sqrt(x^2 + y^2), where x and y are the coefficients of i and j respectively in the given vector.

The magnitude of the given vector is sqrt((-3)^2 + 7^2) = sqrt(9 + 49) = sqrt(58).

Therefore, the unit vector that has the same direction as the given vector is (-3/sqrt(58))i + (7/sqrt(58))j.

Answer 2

The unit vector has the same direction of the given vector but its magnitude is 1.

To find the unit vector divide by the magnitude of the given vector.

Vector - 3i + 7j

Magnitude = |-3i + 7j| = √(3^2 + 7^2) = √(9 + 49) = √58 = 7.62

Then the unit vector is: (-3/√58) i + (7/√58) j