Q140 / 225 · JEE Main 2003 · Mathematics

Consider points A, B, C and D with position vectors $7 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}+7 \hat{\mathrm{k}}, \hat{\mathrm{i}}-6 \hat{\mathrm{j}}+10 \hat{\mathrm{k}},-\hat{\mathrm{i}}-3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}$ and $5 \hat{\mathrm{i}}-\hat{\mathrm{j}}+5 \hat{\mathrm{k}}$ respectively. Then $\mathrm{ABCD}$ is a

  • A
    parallelogram but not a rhombus
  • B
    square
  • Correct answer
    C
    rhombus
  • D
    rectangle

Solution

No option satisfied wrong. $\mathrm{A}=(7,-4,7), \mathrm{B}=(1,-6,10), \mathrm{C}=(-1,-3,4)$ and $\mathrm{D}=(5,-1,5)$ $A B=\sqrt{(7-1)^2+(-4+6)^2+(7-10)^2}=\sqrt{36+4+9}=7$ Similarly $\mathrm{BC}=7, \mathrm{CD}=\sqrt{41}, \mathrm{DA}=\sqrt{17}$

Hence, the correct answer is option: 'C'.

Relevant Questions