Find a unit vector for a⃗ =<1,7>𝑎→=<1,7> in component form.Your final answer should have the denominator rationalized.

A unit vector is a vector of length 1. To find a unit vector with the same direction as a given vector, you divide by the magnitude of the vector.

Step 1: Find the magnitude of the vector a = <1,7> The magnitude (or length) of a vector a = <x, y> is given by √(x² + y²).

So, the magnitude of a = √(1² + 7²) = √(1 + 49) = √50.

Step 2: Divide the vector a by its magnitude To get the unit vector, we divide each component of the vector by the magnitude.

So, the unit vector of a = <1/√50, 7/√50>.

Step 3: Rationalize the denominator To rationalize the denominator, we multiply the numerator and the denominator by √50.

So, the unit vector of a in component form with the denominator rationalized is <√50/50, 7√50/50> = <1/√2, 7√2/2>.