Which of the following vectors is a unit vector?Group of answer choices<-1,0,0><-1,-1,-1><-1,0,1><1,1,1>
Question
Which of the following vectors is a unit vector?Group of answer choices<-1,0,0><-1,-1,-1><-1,0,1><1,1,1>
Solution
A unit vector is a vector of length 1. The length (or magnitude) of a vector <x, y, z> is calculated using the formula sqrt(x^2 + y^2 + z^2).
Let's calculate the length of each vector:
- Vector <-1,0,0>: sqrt((-1)^2 + 0^2 + 0^2) = sqrt(1) = 1
- Vector <-1,-1,-1>: sqrt((-1)^2 + (-1)^2 + (-1)^2) = sqrt(3) ≠ 1
- Vector <-1,0,1>: sqrt((-1)^2 + 0^2 + 1^2) = sqrt(2) ≠ 1
- Vector <1,1,1>: sqrt(1^2 + 1^2 + 1^2) = sqrt(3) ≠ 1
So, the only unit vector among the given options is <-1,0,0>.
Similar Questions
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>
Given the vectors u = (1, 3, 0) and v = (0, 1, -1), which of the following is the cross product of u with v? Group of answer choices (-3, 1, 2) (-3, 1, 1) (2, 2, 2) 3
Which of the following vector is orthogonal to [1−13]⎣⎡ 1−13 ⎦⎤ ?
which of the following vectors are spaces {[1 0 0 1], [0 1 0 0], [1 1 1 1],[0 1 1 1]}
Given v⃗ 𝑣→ with an initial point of ⟨−1,4,6⟩⟨−1,4,6⟩ and a terminal point of ⟨3,3,8⟩⟨3,3,8⟩ , find a unit vector in the same direction as v⃗ 𝑣→.Please be sure your final answer has all denominators rationalized.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.