Question
Download Solution PDFIf \(\rm \vec a.\vec b=0\) and \(\vec a+\vec b\) makes an angle of 30° with \(\vec a\) then
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- Two vectors a and b are perpendicular to each other if a . b = o
Calculations:
Given \(\rm \vec a.\vec b=0\) and \(\vec a+\vec b\) makes an angle of 30° with \(\vec a\)
We can understand it better by the below image.
We have a . b = o, i.e., vector a is perpendicular to vector b
Clearly, from the above diagram Vectors a, b, and a + b together form a right-angled triangle
So, in \(\bigtriangleup PQR\), we have
\(tan \ 30^{o}=\frac{|b|}{|a|}\)
⇒ \(\frac{1}{√{3}}=\frac{|b|}{|a|}\)
⇒ |a| = √3 |b|
Hence, the correct answer is option 2).
Last updated on Jun 6, 2025
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