Will a vector at 45° to the horizontal be larger or smaller than its horizontal and vertical components?

Will a vector at 45° to the horizontal be larger or smaller than its horizontal and vertical components? And by what factor will it be larger or smaller?|||Larger. Just remember the Pythagorean theorem. When you draw a right triangle, the vector will be the hypotenuse. Since it's a 45 degree angle, the vertical and horizontal components are equal. The vector will be larger than them by a factor of square root of 2.|||Larger. It is the vector sum of it's components so it must be larger.





V = sqrt(x^2 + y^2)





since x = y for a 45* angle





V = sqrt(2)x = sqrt(2)y|||each components of all vectors are calculated by multiplying the length of vectors to sine or cosine of the angle. Sines and cosines are always less than 1 so, components are always smaller. It doesn't matter if they are horizontal or vertical