Question

Q4.
The resultant of two vectors P and Q is R. If the magnitude of Q is doubled, the new resultant becomes perpendicular to P. Then the magnitude of R is ?
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Answer 1

Answer:

Explanation:

Let the angle between two vectors  P and Q be α and their resultant is = R

Thus,

R² = P²+Q²+ 2PQcosα  --- (1)

When Q is doubled then let the resultant vector be  R1, thus -

R² = P²+ 4Q²+ 4PQcosα  --- (2)

Again by the given condition  R1 is perpendicular to P, hence -

4Q² = R² + P² --- (3)

Combining equation 2 and 3 we will get -

= R² = P²+ P² + R1² + 4PQcosα  

= 2PQcosα   = -P² --- (4)

Combining equation 1 and 4 we will get -

= R² = P²+ Q² - P²

= R = Q