Question

∆hi users

∆ class 11th non-med.

∆ Physics ques below√√√

∆ if two vectors A and B have resultant of 3i + 2j + 6k and when the two arc added one taken in opp. direction, then the resultant i + 4j - 3k. find the vectors and their magnitudes.

∆ don't spam. . bcz I'll report wrong answer.
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Answer 1

Let the vectors be Axi+Ayj+Azk and Bxi+Byj+Bzk

Resultant = 3i + 2j + 6k = (Ax+Bx)i + (Ay+By)j+(Az+Bz)

= Ax+Bx = 3                         .......(i)

  Ay+By = 2                         .......(ii)

  Az+Bz = 6                         .......(iii)

Now, since one vector has been reversed, it means they are being subtracted

= i + 4j - 3k = Axi+Ayj+Azk-(Bxi+Byj+Bzk)

= (Ax-Bx)i + (Ay-By)j + (Az-Bz)k

= Ax-Bx = 1                          .........(iv)

  Ay-By = 4                         .........(v)

  Az-Bz = -3                        .........(vi)

Solving (i) and (iv), (ii) and (v), and (iii) and (vi) we get

Ax = 2     Bx = 1

Ay = 3     By = -1

Az = 1.5   Bz = 4.5

So, vectors = 2i+3j+1.5k and i-j+4.5k

Magnitudes = √4+9+2.25   and √1+1+20.25

= √15.25   and √22.25

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