KCET · Maths · Vector Algebra
If \(\mathbf{a}\) is a vector perpendicular to both \(\mathbf{b}\) and \(\mathbf{c}\), then
- A \(\mathrm{a} \cdot(\mathrm{b} \times \mathrm{c})=0\)
- B \(a \times(b \times c)=0\)
- C \(a \times(b+c)=0\)
- D \(a+(b+c)=0\)
Answer & Solution
Correct Answer
(B) \(a \times(b \times c)=0\)
Step-by-step Solution
Detailed explanation
Given, \(a\) is perpendicular to both \(b\) and c.
Then, \(\quad a \cdot b=0\) and \(a \cdot c=0...(i)\)
Now, we have
\(a \times(b \times c)=(a \cdot c) b-(a \cdot b) c\)
\(=(0) b-(0) c\) [from Eq. (i)]
\(=0-0=0\)
Then, \(\quad a \cdot b=0\) and \(a \cdot c=0...(i)\)
Now, we have
\(a \times(b \times c)=(a \cdot c) b-(a \cdot b) c\)
\(=(0) b-(0) c\) [from Eq. (i)]
\(=0-0=0\)
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