Question
Download Solution PDFWhat is the value of λ for which the vectors \(\rm 2\hat i - 5\hat j - \hat k\) and \(\rm -\hat i + 4 \hat j + \lambda\hat k\) are perpendicular?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
If vectors \(\rm \vec a\;and\;\vec b\) are perpendicular then \(\rm \vec a \cdot \;\vec b = 0\)
Calculation:
Given: \(\rm 2\hat i - 5\hat j - \hat k\) and \(\rm -\hat i + 4 \hat j + λ\hat k\) are perpendicular
Let \(\rm \vec a = 2\hat i - 5\hat j - \hat k\) and \(\rm \vec b = -\hat i + 4 \hat j + λ\hat k\)
We know that, If vectors \(\rm \vec a\;and\;\vec b\) are perpendicular then \(\rm \vec a \cdot \;\vec b = 0\)
\(\rm \vec a \cdot \vec b = ( 2\hat i - 5\hat j - \hat k) \cdot (-\hat i + 4 \hat j + λ\hat k) = 0\)
⇒ -2 - 20 - λ = 0
⇒ -22 - λ = 0
∴ λ = -22
Last updated on Jul 1, 2025
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