2. Solved Papers
  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2009

  • question_answer
    If the position vectors of three consecutive vertices, of a parallelogram are\[\hat{i}+\hat{j}+\hat{k},\] \[\hat{i}+3\hat{j}+5\hat{k}\] and\[7\hat{i}+9\hat{j}+11\hat{k},\] then the coordinates of the fourth vertex are

    A)  (2, 1, 3)               

    B)  (6, 7, 8)

    C)  (4, 1, 3)         

    D)         (7, 7, 7)

    E)  (8, 8, 8)

    Correct Answer: D

    Solution :

    Let the vertices of a parallelogram are A(1, 1, 1) B(1, 3, 5), C(7, 9, 11) and fourth vertex be D (\[x\], y, z) Midpoint of AC is (4, 5, 6) and midpoint of BD is\[\left( \frac{1+x}{2},\frac{3+y}{2},\frac{5+z}{2} \right)\]. In a parallelogram midpoint of diagonals are coincide. \[\therefore \]  \[\frac{1+x}{2}=4,\frac{3+y}{2}=5,\frac{5+z}{2}=6\] \[\Rightarrow \]               \[x=7,y=7,z=7\]


You need to login to perform this action.
You will be redirected in 3 sec spinner