NIMCET 2026 Mathematics Question 50 with Solution

Question 50

Mathematics Scalar and Vector Products Hard

If \((\vec{a} \times \vec{b}) \times \vec{c}= \vec{a} \times (\vec{b} \times \vec{c})\), then

(A) \(\vec{a}\) and \(\vec{b}\) are collinear

(B) \(\vec{a}\) and \(\vec{b}\) are perpendicular

(C) \(\vec{a}\) and \(\vec{c}\) are collinear

(D) \(\vec{a}\) and \(\vec{c}\) are perpendicular

View Dynamic Solution & Explanation ▼

Correct Solution: Option C

Step-by-step Solution:

Expand the triple product: \[ (a \cdot c) b - (b \cdot c) a = (a \cdot c) b - (a \cdot b) c. \] This simplifies to: \[ (b \cdot c) a = (a \cdot b) c. \] Since \( b \cdot c \) and \( a \cdot b \) are scalar quantities, we conclude that \( a \) and \( c \) are collinear vectors.