What is the area of triangle ABC?

Question 121

HardOriginal question

A triangle has vertices $A(1, 1, 1)$ , $B(2, 3, 3)$ and $C(3, 1, 2)$ .

What is the area of triangle $ABC$ ?

\frac{\sqrt{21}}{2}

Correct answerYour answer

\frac{\sqrt{29}}{2}

Correct answerYour answer

\sqrt{29}

Correct answerYour answer

\frac{29}{2}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

$\overrightarrow{AB} \times \overrightarrow{AC} = 2\hat{i} + 3\hat{j} - 4\hat{k}$ , of magnitude $\sqrt{4 + 9 + 16} = \sqrt{29}$ .
Area $= \frac{\sqrt{29}}{2}$ .

Worth noting

$\sqrt{29}$ is the parallelogram, twice the triangle.

Ten questions from Vectors, at your own pace.

Ten questions from Vectors, at your own pace.