If the formation of a neutron star leads to a supernova explosion, explain why only three of the hundreds of known pulsars are found in supernova remnants.

Explanation:

neutron stars have diameters of about 20km and they are denser than the earth. A rotating neutron star pulsating electromagnetic beam is a named a pulsars but not all neutron stars are pulsars.

Only three of hundreds of known pulsar are found in supernova remnants because as neutron stars gets older, they lose energy and starts to decrease their rotational speeds and the neutron star could not radiate particles and energy for long as a pulsar does. there are less existing pulsars compared to supernova explosion rate because the life time of pulsars is obout 10×10^6 years after the neutron can no longer spin at high speeds to produce beams of particles and energy, almost all the pulsars are older  and spin slow to produce light of visible wavelength or X-ray wavelengths and we only get a pulse of radiation from a neutron star as a pulsar as the beam sweeps over earth.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west