Given two vectors a⃗ =−2.00i^+ 4.00 j^+ 4.00 k^ and b⃗ = 1.00 i^+ 2.00 j^−3.00k^, do the following.

|a⃗ | =

part b

|b⃗ | =

part c
write an expression for the vector difference a⃗ −b⃗ .
enter your answers numerically separated by commas.

x, y,z =

part d
find the magnitude of the vector difference a⃗ −b⃗ .

|a⃗ −b⃗ | =

part e
is this the same as the magnitude of b⃗ −a⃗ ?
is this the same as the magnitude of ?
yes
no

According to social exchange theory, altruistic behaviors benefit the individual who performs them. t/f

The volume of a gas is halved during an adiabatic compression that increases the pressure by a factor of 2.5. what is the specific heat ratio? show the math steps .

Aheat engine running backward is called a refrigerator if its purpose is to extract heat from a cold reservoir. the same engine running backward is called a heat pump if its purpose is to exhaust warm air into the hot reservoir. heat pumps are widely used for home heating. you can think of a heat pump as a refrigerator that is cooling the already cold outdoors and, with its exhaust heat qh, warming the indoors. perhaps this seems a little silly, but consider the following. electricity can be directly used to heat a home by passing an electric current through a heating coil. this is a direct, 100% conversion of work to heat. that is, 19.0 \rm kw of electric power (generated by doing work at the rate 19.0 kj/s at the power plant) produces heat energy inside the home at a rate of 19.0 kj/s. suppose that the neighbor's home has a heat pump with a coefficient of performance of 4.00, a realistic value. note: with a refrigerator, "what you get" is heat removed. but with a heat pump, "what you get" is heat delivered. so the coefficient of performance of a heat pump is k=qh/win. an average price for electricity is about 40 mj per dollar. a furnace or heat pump will run typically 200 hours per month during the winter. what does one month's heating cost in the home with a 16.0 kw electric heater? what does one month's heating cost in the home of a neighbor who uses a heat pump to provide the same amount of heating?