Question
Download Solution PDFDetermine the value of p for which \(p(\hat{i}+\hat{j}+\hat{k})\) is a unit vector?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\(p(\hat{i}+\hat{j}+\hat{k})\) is a unit vector.
Concept:
A unit vector of a vector is a vector of unit magnitude and direction as that of the original vector.
Formula:
The magnitude of a vector aî + bĵ + ck̂ is given by √(a2 + b2 +c2)
Calculation:
The magnitude of given vector \(p(\hat{i}+\hat{j}+\hat{k})\) can be calculated as;
| \(p(\hat{i}+\hat{j}+\hat{k})\)|= |p|√(12 + 12 + 12)
= |p|√3
∵ it is a unit vector:
⇒ |p|√3 = 1
⇒ |p| = 1/√3
or p = ±1/√3
Last updated on May 26, 2025
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