Question
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Complete parts (a) through © below.
a. Find two unit vectors parallel to . 0 of 1
b. Find if is a unit vector.
c. Find all values of a such that is a unit vector.

Ask by Watson Greene. in the United States
Jan 22,2025

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Tutor-Verified Answer

Answer

Part (a): The two unit vectors parallel to are:
Part (b): The values of are:
Part ©: The values of are:

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Beyond the Answer

To solve the problem step by step, let’s complete each part:
a. To find a unit vector parallel to , first we need to find the magnitude of :
Now, to find a unit vector in the same direction, we divide by its magnitude:
The opposite direction of this vector would also be a unit vector:
So, the two unit vectors parallel to are and .
b. To find in the unit vector , we use the unit vector condition which states that its magnitude must equal 1:
This gives us:
Taking the square root:
c. For the vector to be a unit vector, we need its magnitude to equal 1:
Calculating the magnitude gives:
Setting this equal to 1 gives:
Thus, values of can be either positive or negative:

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