Question:
Vectors of magnitude \(3\) and \(4\) are perpendicular. Resultant?
Vectors of magnitude \(3\) and \(4\) are perpendicular. Resultant?
Show Hint
For perpendicular vectors, use Pythagoras theorem:
\[
R=\sqrt{A^2+B^2}
\]
The pair \(3,4,5\) is a common right-triangle result.
Updated On: Jun 3, 2026
- \(5\)
- \(7\)
- \(1\)
- \(12\)
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The Correct Option is A
Solution and Explanation
Concept:
When two vectors are perpendicular to each other, the angle between them is: \(\displaystyle 90^\circ\) For two perpendicular vectors, the magnitude of resultant is found using Pythagoras theorem: \(\displaystyle R=\sqrt{A^2+B^2}\) where, \(A\) and \(B\) are the magnitudes of the two vectors.
Step 1: Write the given vector magnitudes.
First vector magnitude: \(\displaystyle A=3\) Second vector magnitude: \(\displaystyle B=4\)
Step 2: Use resultant formula for perpendicular vectors.
Since the vectors are perpendicular, \(\displaystyle R=\sqrt{A^2+B^2}\) Substitute the values: \(\displaystyle R=\sqrt{3^2+4^2}\)
Step 3: Simplify the expression.
\(\displaystyle R=\sqrt{9+16}\) \(\displaystyle R=\sqrt{25}\) \(\displaystyle R=5\)
Step 4: Final conclusion.
Hence, the resultant of the two perpendicular vectors is: \(\displaystyle \boxed{5}\)
When two vectors are perpendicular to each other, the angle between them is: \(\displaystyle 90^\circ\) For two perpendicular vectors, the magnitude of resultant is found using Pythagoras theorem: \(\displaystyle R=\sqrt{A^2+B^2}\) where, \(A\) and \(B\) are the magnitudes of the two vectors.
Step 1: Write the given vector magnitudes.
First vector magnitude: \(\displaystyle A=3\) Second vector magnitude: \(\displaystyle B=4\)
Step 2: Use resultant formula for perpendicular vectors.
Since the vectors are perpendicular, \(\displaystyle R=\sqrt{A^2+B^2}\) Substitute the values: \(\displaystyle R=\sqrt{3^2+4^2}\)
Step 3: Simplify the expression.
\(\displaystyle R=\sqrt{9+16}\) \(\displaystyle R=\sqrt{25}\) \(\displaystyle R=5\)
Step 4: Final conclusion.
Hence, the resultant of the two perpendicular vectors is: \(\displaystyle \boxed{5}\)
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