Question #fc58a

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Answer 1 · 2017-01-28T04:10:02

Let there be two vectors

$\to P = a ˆ i + b ˆ j + c ˆ k$ $vecP=ahati+bhatj+chatk$

and

$\to Q = e ˆ i + f ˆ j + g ˆ k$ $vecQ=ehati+fhatj+ghatk$

Their resultant will be

$\to R = \to P + \to Q = (a + e) ˆ i + (b + f) ˆ j + (c + g) ˆ k$ $vecR=vecP+vecQ=(a+e)hati+(b+f)hatj+(c+g)hatk$

Let $(a + e) = x; (b + f) = y and (c + g) = z$ $(a+e)=x ;(b+f)=y and (c+g)=z$

So

$\to R = x ˆ i + y ˆ j + z ˆ k$ $vecR=xhati+yhatj+zhatk$

So unit vector parallel to the resultant will be

$ˆ r = \frac{\to R}{∣ ∣ ∣ \to R ∣ ∣ ∣} = \frac{\to R}{\sqrt{x^{2} + y^{2} + z^{2}}}$ $hatr=(vecR)/abs(vecR)=(vecR)/sqrt(x^2+y^2+z^2)$