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What is the unit vector in the direction of 2,2,2?What is the unit vector in the direction of3,3,3?

Short Answer

Expert verified

The unit vector in the direction of2,2,2is13,13,13.

The unit vector in the direction of3,3,3is13,13,13.

Step by step solution

01

Definition of unit vector

The unit vector in the direction of a vector is the vector divided by its magnitude that is given by:

r^=r⇶Är⇶Ä

02

Calculating unit vector for 2,2,2

Take the square root of sum of square of each component of the vector 2,2,2to obtain its magnitude.

22+22+22=23

Divide the vector by its magnitude to compute its unit vector,

r^=2,2,223=13,13,13

Therefore, the unit vector in the direction of2,2,2is13,13,13.

03

Calculating unit vector for 3,3,3

Take the square root of sum of square of each component of the vector 3,3,3to obtain its magnitude.

32+32+32=33

Divide the vector by its magnitude to compute its unit vector.

r^=3,3,333=13,13,13Therefore,theunitvectorinthedirectionof3,3,3is13,13,13

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Most popular questions from this chapter

Figure 1.60 shows the trajectory of a ball travelling through the air, affected by both gravity and air resistance.

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Location

t(s)

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