Write the principal value of

Write the value of

Find the value of a if

If then write the value of x.

If then find the matrix A.

Write the degree of the differential equation

If and are two equal vectors, then write the value of x + y + z.

If a unit vector makes angles with with and an acute angle θ with then find the value of θ.

Find the Cartesian equation of the line which passes through the point (-2, 4, -5) and is parallel to the line

The amount of pollution content added in air in a city due to x-diesel vehicles is given by P(x) = 0.005x^{3} + 0.02x^{2} + 30x. Find the marginal increase in pollution content when 3 diesel vehicles are added and write which value is indicated in the above question.