Question
Download Solution PDFIf aÌ… = 3iÌ… - 2jÌ… + kÌ… and bÌ… = 4iÌ… +3jÌ… - λkÌ… are orthogonal, then λ = ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\(\overrightarrow{a}=3\hat i-2\hat j+\hat k \text{ and }\overrightarrow{B}=4\hat i+3\hat j-\lambda \hat k\) are Orthogonal.
Concept:
Two vectors \(\overrightarrow {a} \text{ and } \overrightarrow{b}\) are considered to be Orthogonal when the angle between them is 90º i.e. vectors are perpendicular to each other.
So, the dot product of both vectors \(\overrightarrow {a} \text{ and } \overrightarrow{b}\) is zero.
- \(\overrightarrow{a}.\overrightarrow{b}=|a||b|cos\theta=|a||b|cos90=0\)
Calculation:
\(\overrightarrow{a}.\overrightarrow{b}=0\)
\((3\hat i-2\hat j+\hat k).(4\hat i+3\hat j-\lambda \hat k)=0\)
\(12-6-\lambda=0\)
\(\implies\lambda=6\)
The correct answer is Option-A-6.
Last updated on May 26, 2025
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