Solving Cartesian Vector Problems: |D|, |E|, D+E, E-D

[mwhowell]

Homework Statement

If D=3i–2j and E=–7i+5j … (a) What is |D|? (b) What is |E|?
(c) What are the vectors D+E and E–D?

!THERE ARE SUPPOSED TO BE HATS OVER THE VARIABLES!


I would put up an attempt at the problem if I even knew how to attempt it.

 

[rock.freak667]

|D| just means the magnitude of the vector D, how do you find the magnitude of a vector?

 

[mwhowell]

so does that just mean D= (3,2)?

 

[rock.freak667]

so does that just mean D= (3,2)?

If you draw the vector. Starting at the origin, you'd go 3 units in the x-direction and 2 units in the negative y-direction. Join the ending of this point back to the origin. The length of the diagonal is the magnitude of the vector.

 

[rwisz]

I can provide some guidance on how to approach these types of Cartesian vector problems. First, it is important to understand the notation being used. The notation |D| and |E| represents the magnitude or length of the vector D and E, respectively. In this case, D=3i–2j means that the vector has a magnitude of 3 in the x direction and -2 in the y direction. Similarly, E=–7i+5j means that the vector has a magnitude of -7 in the x direction and 5 in the y direction.

To find the magnitude of a vector, we can use the Pythagorean theorem, which states that the magnitude (or length) of a vector is equal to the square root of the sum of the squares of its components. In this case, for vector D, the magnitude would be √(3^2 + (-2)^2) = √(9+4) = √13. Similarly, for vector E, the magnitude would be √((-7)^2 + 5^2) = √(49+25) = √74.

For part (a), we can simply substitute the values for D into the formula and find that |D| = √13. Similarly, for part (b), |E| = √74.

For part (c), we can use the vector addition and subtraction rules. Vector addition is performed by adding the corresponding components of the two vectors. In this case, D+E would be (3-7)i + (-2+5)j = -4i + 3j. Vector subtraction is performed by subtracting the corresponding components of the two vectors. In this case, E-D would be (-7-3)i + (5-(-2))j = -10i + 7j.

I hope this helps guide you in solving Cartesian vector problems. Remember to always carefully read and understand the notation being used and apply the appropriate mathematical rules.