📐 Mathematics · Vector Algebra · JEE

The area of the triangle with vertices A(1,1,1), B(2,3,5) and C(1,5,5) is:

Answer: 2√6.

Correct answer: B. 2√6

Explanation: AB = (1,2,4), AC = (0,4,4); AB × AC = (−8,−4,4) with magnitude 4√6. Area = half of this = 2√6.

Triangle law of vector addition: placing vector b at the head of vector a, the diagonal from the start to the final head gives the resultant a + b.

Concept context

Vectors, dot product, cross product, and geometric applications