a rectangular parallelepiped has edge lengths of a b c. (a) Find a vector expres
ID: 1526866 • Letter: A
Question
a rectangular parallelepiped has edge lengths of a b c. (a) Find a vector expressions for the face diagonal (the diagonal of one of the rectangular faces of the parallelepiped) labelled F (b) What is the magnitude of each? (c) Find a vector expression for the diagonal of the parallelepiped (from one corner to the opposite corner) labelled D . (d) Using the results of (a) and (c), find the area of the body diagonal A, the plane that goes from one edge to the opposite one, using the fact that the diagonal will make a triangle with a face diagonal and one of the edges.
the correct answer for D is b(a^2+c^2 ) but can you asnwer all part a b c and d with the complete solution thanks!
b D F A CExplanation / Answer
(a) the face diagonal in vector form can be written using the triangle law of vector addition
F= ai + bj
other face diagonals are ai+ ck and bj + ck.
i , j and k are the unit vectors along x , y and z axis.
(b) for the magnitude we use the pythagoras theorem,so the magnitude of face diagonals are sqrt(a2+b2),
sqrt(a2+c2), sqrt(b2+c2)
(c)the body diagonal D = ai + bj+ ck.
magnitude of D= sqrt(a2 +b2+c2)
(d)are of diagonal= area of triangle= 1/2 * base * height
area= (1/2)* b*(a^2+c^2 )
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