Consider points A,B,C and D with position vectors 7 i-4 j+7 k, i-6 j+10 k, - i-3 j+4 k and…

Question

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

Accepted Answer

$$AB=\sqrt{6^2+2^2+3^2}=\sqrt{49}=7,\quad BC=\sqrt{2^2+3^2+6^2}=7,\quad CD=\sqrt{6^2+2^2+1^2}=\sqrt{41},\quad DA=\sqrt{2^2+3^2+2^2}=\sqrt{17}$$

Since the four sides are not all equal (and other shape conditions fail), $ABCD$ does not match any of the named quadrilaterals --- the answer is None.

Solutions · 1