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Statement 1 : If |veca + vecb| = |veca -...

Statement 1 : If `|veca + vecb| = |veca - vecb|`, then `veca and vecb` are perpendicular to each other.
Statement 2 : If the diagonals of a parallelogram are equal in magnitude, then the parallelogram is a rectangle.

A

Both the statements are true, and Statement 2 is the correct explanation for Statement 1.

B

Both the statements are true, but Statement 2 is not the correct explanation for Statement 1.

C

Statement 1 is true and Statement 2 is false.

D

Statement 1 is false and Statement 2 is true.

Text Solution

Verified by Experts

The correct Answer is:
A
`veca + vecb = veca - vecb` are the diagonals of a parallelogram whose sides are `veca and vecb`.
`" " |veca + vecb| = |veca - vecb|`
Thus, diagonals of the parallelogram have the same length.
Hence, the parallelogram is a rectangle, i.e., `veca bot vecb`
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