NIMCET 2020 Mathematics Question 36 with Solution

Question 36

Mathematics Scalar and Vector Products Hard

Vertices with the position vectors î - 2ĵ + 2k̂, 2î + ĵ - k̂ and 3î - ĵ + 2k̂ form a triangle. This triangle is:

(A) Equilateral triangle.

(B) Right angle triangle.

(C) Two sides are equal in length.

(D) None of the above.

View Dynamic Solution & Explanation ▼

Correct Solution: Option B

Step-by-step Solution:

Suppose the vertices are \( A \), \( B \), and \( C \), then: \[ \text{AB} = i - 3j - 3k \] \[ \text{BC} = 2i + j \] \[ \text{CA} = i - 2j + 3k \] Here: \[ \text{BC} \cdot \text{AC} = 2 - 2 = 0 \] Hence, the triangle is right-angled.