- #1
ttpp1124
- 110
- 4
- Homework Statement
- I solved it, but can someone lmk if there's a way to see if I'm correct..? Thank you in advance!
- Relevant Equations
- n/a
Proving that this vector eqn is correct...
- Thread starter ttpp1124
- Start date
-
- Tags
- Vector
In summary, to prove that a vector equation is correct, one can use methods such as verifying vector properties, applying geometric concepts, or using algebraic manipulation. Some helpful vector properties include the commutative, associative, distributive, and scalar multiplication properties. Geometric concepts such as the triangle law, parallelogram law, and vector projections can also be used. Algebraic manipulation involves rearranging and simplifying equations using algebraic rules, which can help demonstrate equality between both sides of the vector equation. To avoid common mistakes, it is important to consider all vector properties, carefully check each step of the proof, and use proper notation for vectors.
- #2
- 5,730
- 2,987
I agree with your solution.
- #3
ttpp1124
- 110
- 4
Thank youCharles Link said:
- #4
archaic
- 688
- 214
So that you do it quicker next time, remember that the directional vector of a vector ##\vec u## perpendicular to a vector ##\vec v = (a,\,b)## is always##(-b,\,a)##. Knowing that, you can directly say that the directional vector of ##\vec q## is ##(-2,\,-3)=-(2,\,3)##, thus ##\vec q=(c,\,d)-s(2,\,3)##.
Yes it is negative the one you found, but consider both cases when ##s## is positive and when it is negative; we'll reach the same points.
Yes it is negative the one you found, but consider both cases when ##s## is positive and when it is negative; we'll reach the same points.
FAQ: Proving that this vector eqn is correct...
How do you prove that a vector equation is correct?
To prove that a vector equation is correct, you can use various methods such as substitution, graphical representation, or algebraic manipulation. These methods involve showing that both sides of the equation are equal to each other, thus proving its correctness.
Can a vector equation be incorrect?
Yes, a vector equation can be incorrect if it does not satisfy the properties of vector operations, such as commutativity and associativity. It can also be incorrect if there are errors in the calculations or if the vectors used are not in the correct form.
What are the properties of vector operations?
The properties of vector operations include commutativity, associativity, and distributivity. Commutativity states that the order of vector operations does not affect the result, while associativity states that the grouping of vector operations does not affect the result. Distributivity states that vector operations can be distributed over addition or subtraction.
How do you know if a vector equation is valid?
A vector equation is valid if it follows the properties of vector operations and if it satisfies the given conditions. This means that the equation must be consistent with the rules of vector operations and that the vectors used must be in the correct form.
Can a vector equation have more than one solution?
Yes, a vector equation can have more than one solution. This can happen when there are multiple sets of vectors that satisfy the equation or when the equation represents a line or plane with infinite solutions. In such cases, it is important to specify the conditions or restrictions to find a unique solution.