5. the analytical method of adding vectors expressed in terms of their components may be applied to vectors in three dimensions, for which graphical work is inconvenient. find the magnitude of the resultant of the vectors a = i12 —j37 + k58 and b = i5 + j30 — k42, where i, j, and k are unit vectors along the x, y, and z axes, respectively

The velocity of a curling stone is due east. what will be the direction of the momentum of the curling stone as it moves?

One day, after pulling down your window shade, you notice that sunlight is passing through a pinhole in the shade and making a small patch of light on the far wall. you see that the patch of light seems to be a circular diffraction pattern. it appears that the central maximum is about 1 cm across and you estimate that the distance from the window shade to the wall is about 3 m. what is (a) the average wavelength of sunlight? (b) the diameter of the pinhole?

Your target variable is δf, the magnitude of the difference in frequency between the waves emitted from the sonar device and the waves received by the device after reflecting off the whale. write an expression for δf in terms of the relevant frequencies using the subscript notation introduced above.