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if P+Q=P-Q ,then...

if `P+Q=P-Q` ,then

A

P=0

B

Q=0

C

P=1

D

|Q|=1

Text Solution

AI Generated Solution

The correct Answer is:
To solve the equation \( P + Q = P - Q \), we can follow these steps: ### Step 1: Rearranging the Equation Start by rearranging the equation to isolate the terms involving vector \( Q \): \[ P + Q = P - Q \] Subtract \( P \) from both sides: \[ Q = -Q \] ### Step 2: Adding \( Q \) to Both Sides Now, add \( Q \) to both sides of the equation: \[ Q + Q = 0 \] This simplifies to: \[ 2Q = 0 \] ### Step 3: Solving for \( Q \) Now, divide both sides by 2: \[ Q = 0 \] ### Step 4: Substituting \( Q \) Back Now that we have found \( Q = 0 \), we can substitute this back into the original equation to check if it holds: \[ P + 0 = P - 0 \] This simplifies to: \[ P = P \] This is always true, confirming our solution. ### Conclusion Since we found \( Q = 0 \), we can conclude that the only possible solution is when vector \( Q \) is the zero vector. The value of vector \( P \) can be any vector, including the zero vector. ### Final Answer Thus, the answer is: - \( Q = 0 \) - \( P \) can be any vector (including \( P = 0 \)).
To solve the equation \( P + Q = P - Q \), we can follow these steps: ### Step 1: Rearranging the Equation Start by rearranging the equation to isolate the terms involving vector \( Q \): \[ P + Q = P - Q \] Subtract \( P \) from both sides: ...
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