Loppyfoot said:Homework Statement
Find the magnitude and direction of A + B for the following vectors.
A = -4 i - 1 j, B = 8 i -2 j
How do I find the magnitude of A+B, and also the degree clockwise from the +x direction?
Loppyfoot said:So would it be 4i - 3j? On my webassign homework, it has to be a single numerical value.
The magnitude of A+B can be found using the Pythagorean theorem, where the square root of the sum of the squares of the individual vector components is taken. In other words, the magnitude is equal to the square root of (A^2 + B^2).
The direction of A+B can be found using trigonometric functions such as sine, cosine, and tangent. First, find the angle between the two vectors using the dot product formula. Then, use inverse trigonometric functions to find the direction in terms of degrees or radians.
A unit vector is a vector with a magnitude of 1. It is used to represent the direction of a vector without considering its magnitude. Unit vectors are often represented by the lowercase letter "u" with a vector symbol on top (û).
To calculate the unit vector of A+B, first find the magnitude of A+B using the Pythagorean theorem. Then, divide each of the individual vector components by the magnitude to get the unit vector in the same direction as A+B.
Sure, let's say A = (3, 4) and B = (5, 2). The magnitude of A+B would be √(3^2 + 5^2) = √34. To find the direction, we can use the dot product formula: A ⋅ B = |A| |B| cos θ. Plugging in the values, we get 3(5) + 4(2) = √34 |B| cos θ. Solving for θ, we get cos θ = 3/√34. Using an inverse cosine calculator, we find that θ ≈ 58.63 degrees. Therefore, the direction of A+B is 58.63 degrees from the positive x-axis.