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Motion In A Plane

Question
CBSEENPH11018070

If straight A with rightwards arrow on top space and space straight B with rightwards arrow on top are orthogonal , then prove that 
                  open vertical bar straight A with rightwards arrow on top plus straight B with rightwards arrow on top close vertical bar space equals space square root of straight A squared plus straight B squared end root

Solution

Magnitude of resultant of two vectors straight A with rightwards arrow on top space and space straight B with rightwards arrow on top acting at angle straight theta is given by, 
              space space open vertical bar straight A with rightwards arrow on top plus straight B with rightwards arrow on top close vertical bar space equals space square root of straight A squared plus straight B squared plus 2 ABcosθ end root 
Here, straight A with rightwards arrow on top space and space straight B with rightwards arrow on top are orthogonal, therefore straight theta equals 90 degree 
Therefore, 
            open vertical bar straight A with rightwards arrow on top plus straight B with rightwards arrow on top close vertical bar space equals space square root of straight A squared plus straight B squared plus 2 ABcos 90 degree end root 
                      equals square root of straight A squared plus straight B squared end root 

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