Vector Algebra Question 36
Question: The adjacent sides AB and AC of a triangle ABC are represented by the vectors $ -2\hat{i}+3\hat{j}+2\hat{k} $ and $ -4\hat{i}+5\hat{j}+2\hat{k} $ respectively. The area of the triangle ABC is
Options:
A) 6 square units
B) 5 square units
C) 4 square units
D) 3 square units
Show Answer
Answer:
Correct Answer: D
Solution:
- [d] Area of $ \Delta ,ABC=\frac{1}{2}( \overrightarrow{AB}\times \overrightarrow{AC} ) $ $ =\frac{1}{2} \begin{vmatrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ -2 & 3 & 2 \\ -4 & 5 & 2 \\ \end{vmatrix} $ $ =\frac{1}{2}[ \hat{i}(6-10)-\hat{j}(-4+8)+\hat{k}(-10+12) ] $ $ =\frac{1}{2}[ -4\hat{i}-4\hat{j}+2\hat{k} ] $ $ =\frac{1}{2}\sqrt{16+16+4}=\frac{1}{2}\sqrt{36} $ $ =\frac{1}{2}\times 6 $ $ =3 $ square units
BETA
