Homework Help for Calculus

 Find the equation of the plane in 𝑥𝑦𝑧���-space through the point 𝑃=(4,5,3)�=(4,5,3) and perpendicular to the vector 𝐧=(4,5,4)�=(4,5,4).

Find the equation of the plane through the point 𝑃=(3,4,4)�=(3,4,4) and parallel to the plane 2𝑥−3𝑦−3𝑧=5.

Write the line through 𝑝=(3,−1,−4)�=(3,−1,−4) in the direction of 𝑣⎯⎯⎯=⟨−4,−4,0⟩�¯=⟨−4,−4,0⟩ in vector parametric form:

A trough is 7 meters long, 1.5 meters wide, and 1 meters deep. The vertical cross-section of the trough parallel to an end is shaped like an isoceles triangle (with height 1 meters, and base, on top, of length 1.5 meters). The trough is full of water (density 1000kg/m^3). Find the amount of work in joules required to empty the trough by pumping the water over the top. (Note: Use g=9.8m/s^2 as the acceleration due to gravity.)

The vector in the opposite direction to 𝑢⎯⎯⎯=⟨−2,3⟩�¯=⟨−2,3⟩ and of half its length is

For what values of 𝑡� and 𝑠� does the equality

hold true?

Find a vector 𝐚� with representation given by the directed line segment 𝐴𝐵−→−��→, where 𝐴(−6,−6)�(−6,−6) and 𝐵(2,5)�(2,5).