kasda-1 said:Homework Statement
What value of c will make these two vectors parallel?
Homework Equations
3i + 2j + 9k = w
5i - j + ck = v
The Attempt at a Solution
I tried too find a common factor to multiply by the w vector to get the components of the v vector, but no luck.
3i (5/3) + 2j (5/3) +9k (5/3) = 5i + 10/3 j + 45/3 k ≠ 5i - j +ck
Dick said:Would that lead you to conclude that there is no value of c that will make them parallel? Because that would be correct.
Two vectors are parallel if they have the same direction or are in the same line, even if they have different magnitudes.
You can determine if two vectors are parallel by finding their direction or slope. If they have the same direction or slope, they are parallel. You can also use the dot product to determine if two vectors are parallel.
If two vectors are parallel, then they are scalar multiples of each other. This means that multiplying one vector by a scalar value will result in the other vector.
No, two non-zero vectors cannot be parallel. For two vectors to be parallel, they must have the same direction or slope, and non-zero vectors have different directions or slopes.
Understanding parallel vectors is important in many areas of science and mathematics, such as physics, engineering, and geometry. It allows us to analyze and solve complex problems involving direction and magnitude. Additionally, parallel vectors have applications in fields such as computer graphics and data science.