Q.43. Vectors

Question 43.
A vector (A) is added to (B)=6i - 8j. The resultant vector is in the positive x direction and has a magnitude equal to that of (A). What is the magnitude and direction of (A)?

Answer 43.
Let vector A = xi + yj
Adding B = 6i - 8j, the resultant is
(x + 6)i + (y - 8)j

As the resultant is in positive x direction, y - 8 = 0 which gives y = 8.
As the magnitudes of A and the resultant are the same,
x^2 + y^2 = (x + 6)^2 ( because y - 8 = 0 )
12x = y^2 - 36 = (8)^2 - 36 = 28 which gives x = 7/3

Thus vector A = (7/3) i + 8j
The magnitude of A = sqrt [(7/3)^2 + (8)^2] = 25/3
A makes with positive x direction angle tan^(-1) [8/(7/3)]
=tan^(-1) (24/7)

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