0

I am having trouble in this question:

The cosine of angle between two diagonals of a cube is:

  • a) $\frac{1}{2}$
  • b)$\frac{1}{3}$
  • c)$\frac{2\sqrt{2}}{3}$
  • d)None of the above

Upon solution I found out that the only possible answers are $\frac{1}{2}$, $\frac{2\sqrt{2}}{3}$, and 0 so option B should be the answer but the sheet tells the answer to be option A. Please can anyone help me with this?

PS. Please do let me know if you guys want to see my solution or if you guys think the answer mentioned in the sheet is wrong, also I have to solve this question by assuming position vectors of the vertices.

pawel
  • 989
Sarthak Katiyar
  • 3

1 Answers1

1

Two diagonal vectors are $\hat A$= <1,1,1>, $\hat B$=<-1,1,1>

cos $\theta$ = $\frac{\hat A.\hat B}{|\hat A|.|\hat B|}$= $\frac{1}{\sqrt(3).\sqrt(3)}$=$\frac{1}{3}$

Star Bright
  • 2,338