Vector Algebra
Vector Algebra
nta_abhyas_2025
Grade 12
Question:
If $\vec{m}$, $\vec{n}$, $\vec{o}$ are 3 unit vectors such that $\vec{m} \cdot \vec{n} = 0$, $\vec{n} \cdot \vec{o} = 0$ and the angle between $\vec{m}$ and $\vec{o}$ is $\frac{\pi}{6}$, then the value of $|\vec{m} \times \vec{n} - \vec{n} \times \vec{o}|$ is equal to
Step-by-Step Solution
Key Concept: Scalar triple products have the property $[\vec{a}\vec{b}\vec{c}] = [\vec{b}\vec{c}\vec{a}] = [\vec{c}\vec{a}\vec{b}]$ and change sign under swap of two vectors.
Using the properties of scalar and vector triple products along with the given vector relationships, the computation reduces to evaluating a determinant or using the distributive properties of the cross product. The final answer simplifies to the value 1.
Correct Answer: 1