NDA 2023 Maths · Mathematics · Vector Algebra · easy

Hat i·(hat j×hat k)=1. 2. For any vector vec a, vec a×vec a=|vec a|^2.

Single correct option

Consider the following statements:
1.

\hat i\cdot(\hat j\times\hat k)=1

.
2. For any vector

\vec a

\vec a\times\vec a=|\vec a|^2

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

Show answer and solution

Answer: (A) 1 only

Since

\hat j\times\hat k=\hat i

, we get

\hat i\cdot\hat i=1

, so Statement 1 is true. The cross product of a vector with itself is the zero vector (the angle is

0

), not

|\vec a|^2

(which is

\vec a\cdot\vec a

), so Statement 2 is false.

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