Which of the following is the unit vector representation of the vector <3, -2, -5>?Group of answer choices<-0.49, -0.32, -0.81><0.49, 0.32, 0.81><-0.49, 0.32, 0.81><0.49, -0.32, -0.81>
Question
Which of the following is the unit vector representation of the vector <3, -2, -5>?Group of answer choices<-0.49, -0.32, -0.81><0.49, 0.32, 0.81><-0.49, 0.32, 0.81><0.49, -0.32, -0.81>
Solution
To find the unit vector representation of a vector, we first need to find the magnitude of the vector. The magnitude (or length) of a vector <x, y, z> is given by the formula sqrt(x^2 + y^2 + z^2).
Step 1: Calculate the magnitude of the vector <3, -2, -5> Magnitude = sqrt((3)^2 + (-2)^2 + (-5)^2) = sqrt(9 + 4 + 25) = sqrt(38)
Step 2: Divide each component of the vector by the magnitude to get the unit vector. Unit vector = <3/sqrt(38), -2/sqrt(38), -5/sqrt(38)>
To match this with the given options, we can approximate sqrt(38) to 6.16.
So, the unit vector is approximately <-0.49, 0.32, 0.81>.
Therefore, the correct answer is <-0.49, 0.32, 0.81>.
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