Vectors 3 Question 26

26. If $\overrightarrow{\mathbf{X}} \cdot \overrightarrow{\mathbf{A}}=0, \overrightarrow{\mathbf{X}} \cdot \overrightarrow{\mathbf{B}}=0, \overrightarrow{\mathbf{X}} \cdot \overrightarrow{\mathbf{C}}=0$ for some non-zero vector $\overrightarrow{\mathbf{X}}$, then $[\overrightarrow{\mathbf{A}} \overrightarrow{\mathbf{B}} \overrightarrow{\mathbf{C}}]=0$.

(1983, 1M)

Show Answer

Answer:

Correct Answer: 26. True

Solution:

  1. Since, $\overrightarrow{\mathbf{X}} \cdot \overrightarrow{\mathbf{A}}=\overrightarrow{\mathbf{X}} \cdot \overrightarrow{\mathbf{B}}=\overrightarrow{\mathbf{X}} \cdot \overrightarrow{\mathbf{C}}=\mathbf{0}$

$\Rightarrow \overrightarrow{\mathbf{X}}$ is perpendicular to $\overrightarrow{\mathbf{A}}, \overrightarrow{\mathbf{B}}, \overrightarrow{\mathbf{C}}$, therefore $[\overrightarrow{\mathbf{A}} \overrightarrow{\mathbf{B}} \overrightarrow{\mathbf{C}}]=0$

Hence, given statement is true.



NCERT Chapter Video Solution

Dual Pane