Belongs to the topic of basic vectors

Question

Let one vertex of cuboid whose faces are parallel to coordinate planes is (1,2,3). If mid-point of one of the edge in (0,0,0) then find possible

(a) total surface area of cuboid

(b) length of body diagonal

Answer 1

Let l, b & h be dimensions of cuboid.

Mid-point of edge whose length is l is (0, 0, 0).

\(\therefore (\frac l2 , b, h) = (1,2,3)\)

⇒ \(l = 2, b = 2, h = 3\)

(a) Total surface area = 2(lb + bh + hl) = 2(4 + 6 + 6) = 32 unit².

(b) Length of body diagonal = \(= \sqrt{l^2 + b^2 + h^2} = \sqrt{4 + 4 + 9} = \sqrt{17}\) unit.