5. Since 𝒖 ∙ 𝒖 = ||𝒖||^2, we can take the square root of both sides to get ||𝒖|| = √(𝒖 ∙ 𝒖) = √45. Therefore, the magnitude of u is √45.
6. The distance between the two points can be found using the distance formula:
d = √[(5-1)^2 + (9-3)^2] = √52
Since the force and displacement are in the same direction, the work done is given by:
W = ||F|| d = √(2^2 + 3^2) √52 ≈ 35.72 foot-pounds
7. To determine if 𝒖 and 𝒗 are orthogonal, we can take their dot product:
𝒖 ∙ 𝒗 = (-2)(1) + (1)(2) = 0
Since the dot product is 0, we know that 𝒖 and 𝒗 are orthogonal, meaning they are perpendicular to each other.
5. Find the magnitude of u given that 𝒖 ∙ 𝒖 = √45
6.a force is given by the vector F=(2,3) and moves an object from the point (1,3) to (5,9). The force and displacement are in the same direction. Find the work in foot-pounds.
7.determine if u=-2i+j and v=i+2j are orthogonal, parallel, or neither. Show all your work that supports your answer.
5 answers
if 𝒖 ∙ 𝒖 = √45 then |u| = ∜45
No, if 𝒖 ∙ 𝒖 = √45, then ||𝒖|| = √(𝒖 ∙ 𝒖) = √45. The square root of 45 is not a perfect fourth power, so the magnitude of 𝒖 cannot be expressed as the fourth root of 45.
what rot. If 𝒖 ∙ 𝒖 = |u|^2 = √45 then |u| = ∜45
If |u| = √45 then 𝒖 ∙ 𝒖 = 45
If |u| = √45 then 𝒖 ∙ 𝒖 = 45
You are correct, my apologies for the confusion.
If 𝒖 ∙ 𝒖 = |u|^2 = √45, then |u| = √(𝒖 ∙ 𝒖) = √45, as you mentioned.
And if |u| = √45, then 𝒖 ∙ 𝒖 = |u|^2 = (√45)^2 = 45.
If 𝒖 ∙ 𝒖 = |u|^2 = √45, then |u| = √(𝒖 ∙ 𝒖) = √45, as you mentioned.
And if |u| = √45, then 𝒖 ∙ 𝒖 = |u|^2 = (√45)^2 = 45.