How Do You Solve for m and n to Make mA + nB + C Parallel to the Y-Axis?

In summary, the conversation discusses the process of finding the values of m and n in order to make the vector mA + nB + C parallel to the y-axis. The solution involves using the dot product or cross product and ensuring that the resulting vector has a y-component of 0 and x and z components of 0.
  • #1
Greychu
14
0
If A = 5ax + 3ay + 2az
B = -ax + 4ay + 6az
C = 8ax + 2ay

Find the value of m and n such that mA + nB + C is parallel to y-axis.

My problem is I did not know how to determine the m and n value because I did not know what method can use to solve for mA + nB + C parallel to y axis. Does it means that the vector line of mA + nB + C must be a straight line parallel to y axis?

mA + nB + C
= (5m - n + 8)ax + (3m + 4n + 2)ay + (2m + 6n)az

To use dot product means that (mA + nB + C) dot (??) = 1
cross product means that (mA + nB + C) cross (??) = 0

I don't know the ?? is stand for what... can someone pls help me?
 
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  • #2
mA + nB + C should be a vector that should have same direction as <0,1,0>.

What that means is that other than y component not equals zero, x and z components should be zero.
 
  • #3
Thanks, now I am able to solve the question :D
 

1. How do I know which operations to use in a vector question?

In a vector question, you typically use operations such as addition, subtraction, multiplication, and division. The specific operation you use will depend on what the question is asking and the information given. You may also need to use concepts like dot product or cross product in more advanced vector questions.

2. What is the difference between scalar and vector quantities?

Scalar quantities only have magnitude, while vector quantities have both magnitude and direction. Examples of scalar quantities include temperature and mass, while examples of vector quantities include velocity and force.

3. How do I find the magnitude of a vector?

To find the magnitude of a vector, you can use the Pythagorean theorem: magnitude = √(x^2 + y^2 + z^2), where x, y, and z represent the components of the vector. Alternatively, you can use the formula |a| = √(a1^2 + a2^2 + ... + an^2) where a1, a2, ..., an are the components of the vector.

4. How can I determine the direction of a vector?

The direction of a vector can be determined using trigonometric functions, such as tangent, cosine, and sine. You can also use the inverse tangent function to find the angle between the vector and a reference axis.

5. Can you give an example of a real-world application of vectors?

Vectors are commonly used in physics and engineering to represent forces and motion. For example, in a game of billiards, the direction and magnitude of the cue ball's velocity can be represented by a vector. In navigation, vectors are used to represent the direction and speed of a moving object, such as a ship or airplane.

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