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Standard XII

Physics

Vector Addition

If A = B + ...

Question

If $\to A = \to B + \to C$ and $\to A, \to B, \to C$ has scalar magnitudes of 5, 4, 3 units respectively then the angle between $\to A$ and $\to C$ is

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Solution

$\to A = \to B + \to C$
$\to A - \to C = \to B$
Taking self scalar product on both sides-
$(A - C) . (A - C) = (B . B)$
$(A . A - C . A - A . C + C . C) = | B |^{2}$
$| A |^{2} - 2 A C + | C |^{2} = | B |^{2}$
$5^{2} - 2 | A | | C | cos θ + 3^{2} = 4^{2}$
$18 - 2 (5) (3) cos θ = 0$
$18 - 30 cos θ = 0$
$cos θ = \frac{3}{5}$
$θ = {cos}^{- 1} \frac{3}{5}$

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If →A=→B+→C and →A,→B,→C has scalar magnitudes of 5, 4, 3 units respectively then the angle between →A and →C is

→A=→B+→C →A−→C=→BTaking self scalar product on both sides-(A−C).(A−C)=(B.B)(A.A−C.A−A.C+C.C)=|B|2|A|2−2AC+|C|2=|B|252−2|A||C|cosθ+32=4218−2(5)(3)cosθ=018−30cosθ=0cosθ=35θ=cos−135

If $\to A = \to B + \to C$ and $\to A, \to B, \to C$ has scalar magnitudes of 5, 4, 3 units respectively then the angle between $\to A$ and $\to C$ is