Question

A vector u and a line in ² are given. Compute the orthogonal projection w of u on , and use it to compute the distance d from the endpoint of u to .

u = [5] and y = 0
[0]

Answer 1

The resultant magnitude after adding three vectors of equal magnitude but different directions (northeast, northwest, and southwest) is 5 units, as two vectors cancel each other out and the third remains unaffected.

Step-by-step explanation:

The subject of the question is the computation of the orthogonal projection of a vector onto a line and the use of this to find the distance from a point to a line in a two-dimensional space. However, there is a discrepancy, as the vectors provided (u and V) do not directly relate to the initial question, but rather illustrate a separate problem about vector addition. I will address the vector addition:

When adding three vectors of equal magnitude but different directions, as described – U pointing northeast, V pointing southwest, which is exactly opposite to U, and another vector W pointing northwest – the resultant vector can be determined by vector addition.

Vectors U and V will cancel each other out because they are in opposite directions. The third vector, W, will not be cancelled out, as it has a different direction. Therefore, the magnitude of the resultant vector will be the same as that of vector W, which is 5 units.

The answer is option b: 5 units, since two vectors cancel each other out, leaving the third vector's magnitude unchanged.