**Question :**
Sum of two vectors A and B is equal to A. Difference of these two vectors is equal to 2A. If A=4 find the MAGNITUDE of vector B.

a)3√2

b)6√2

c)2√6

d)3√6

Question of GIKI test 2012.

In terms of rectangular components we can write:

A =√ A

B=√ B

Given:

A + B = A

it means

√( A

Squaring Both sides, we get

A

Also

A-B = 2A

A-B = 8

√( A

Squaring Both sides, we get

A

Adding equation i and ii we get

2( A

16 + B

B

B

B = √24 = √4x6 = 2√6

**Solution:**In terms of rectangular components we can write:

A =√ A

^{2}_{x}+ A^{2}_{y}B=√ B

^{2}_{x}+ B^{2}_{y}Given:

A + B = A

it means

√( A

^{2}_{x}+ A^{2}_{y}) + √( B^{2}_{x}+ B^{2}_{y }) = 4Squaring Both sides, we get

A

^{2}_{x}+ A^{2}_{y}+ B^{2}_{x}+ B^{2}_{y }+ 2√( A^{2}_{x}+ A^{2}_{y})( B^{2}_{x}+ B^{2}_{y }) = 16 (equation i)Also

A-B = 2A

A-B = 8

√( A

^{2}_{x}+ A^{2}_{y}) - √( B^{2}_{x}+ B^{2}_{y }) = 8Squaring Both sides, we get

A

^{2}_{x}+ A^{2}_{y}+ B^{2}_{x}+ B^{2}_{y }- 2√( A^{2}_{x}+ A^{2}_{y})( B^{2}_{x}+ B^{2}_{y }) = 64 (equation ii)Adding equation i and ii we get

2( A

^{2}_{x}+ A^{2}_{y}+ B^{2}_{x}+ B^{2}_{y}) = 8016 + B

^{2}_{x}+ B^{2}_{y}= 40B

^{2}_{x}+ B^{2}_{y}= 24B

^{2}= 24B = √24 = √4x6 = 2√6

what the hell was that? :O

ReplyDelete@ayesha this was one of the question which was in test of GIKI last year :D

ReplyDeleteand this is the hardest and worst thing one would ever wish to see, if the test goes this way, we shouldnt even bother about studying for it because its already a fail fail attempt

ReplyDeletewell in Giki u have to face the questions like these . It will be teh hardest test u'll ever see . The way to get through this test is to clear ur concepts..

ReplyDeleteu substituted 16 but why ?

ReplyDeletein last part of the question ?

magnitude of A is equal to 16 .

ReplyDeleteAwesome site you have here but I was curious if you knew

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WE are supposed solve it in a minute?

ReplyDeletewe are supposed to solve it in a minute?

ReplyDeleteI have found a short method for this as well. Will add that too.

ReplyDelete