Each question has four choices a, b, c, and d, out of which only one is correct. Each question contains STATEMENT 1 and STATEMENT 2. 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. A vector has components `p` and 1 with respect to a rectangular Cartesian system. The axes are rotted through an angel `alpha` about the origin the anticlockwise sense. Statement 1: IF the vector has component `p+2` and 1 with respect to the new system, then `p=-1.` Statement 2: Magnitude of the origin vector and the new vector remains the same.

Options

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.

Answer

A

Explanation

`sqrt((p+2)^(2)+1)= sqrt(p^(2)+1)`
or `p^(2)+4 +4p +1 = p^(2)+1`
or `4p=-4`
or `p=-1`
Hence, a is the correct option.