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Find a unit vector that has the same direction as the given vector: (−8, 4, 8).
Vectors have many applications in the field of engineering and physics. Many problems related to kinematics and laws of motion are solved by using vectors.
Answer: A unit vector with the same direction as (−8, 4, 8) is (−2/3, 1/3, 2/3).
Let's solve this step by step in detail.
Explanation:
Given, A0 = (−8, 4, 8)
Let A1 be the unit vector in the same direction as A0
Hence, A1 = (−8u, 4u, 8u)
The length of a above vector is given by √[(-8)2 u2 + 42 u2 + 82 u2] = u ⋅ √144 = 12u
Since, we have to find the unit vector, the length should be equal to one:
⇒ 12u = 1
u = 1/12
A1 = (−8 × 1/12, 4 × 1/12, 8 × 1/12)
Simplifying the above vectors, we get:
A1 = (−2/3, 1/3, 2/3)
Thus, a unit vector with the same direction as (−8, 4, 8) is (−2/3, 1/3, 2/3).
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