NDA 2025 Maths · Mathematics · Vector Algebra · easy

The scalar triple product of three coplanar vectors is zero. 2. For any vector vec a, vec a×vec a is the zero vector.

Single correct option

Consider the following statements:
1. The scalar triple product of three coplanar vectors is zero.
2. For any vector

\vec a

\vec a\times\vec a

is the zero vector.
Which of the statements given above is/are correct?

A. $1$ only
B. $2$ only
C. Both $1$ and $2$
D. Neither $1$ nor $2$

Show answer and solution

Answer: (C) Both $1$ and $2$

The scalar triple product equals the volume of the parallelepiped formed by the vectors, which is zero when they lie in a plane, so statement 1 is correct. The cross product has magnitude

|\vec a||\vec a|\sin0^\circ=0

, so

\vec a\times\vec a=\vec 0

: statement 2 is also correct.

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