Vectors 1 Question 16

17. A vector a has components 2p and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If, with respect to the new system, a has components p+1 and 1 , then

(1986, 2M)

(a) p=0

(b) p=1 or p=13

(c) p=1 or p=13

(d) p=1 or p=1

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Answer:

Correct Answer: 17. (9)

Solution:

  1. Here, a=(2p)i^+j^, when a system is rotated, the new component of a are (p+1) and 1 .

i.e. b=(p+1)i^+j^|a|2=|b|2

or 4p2+1=(p+1)2+14p2=p2+2p+1

3p22p1=0(3p+1)(p1)=0

p=1,1/3



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