The magnitude of vectors A- B- and C- are 3- 4 and 5 units respectively- if A-B- - C- find the angle between A- and B-

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Definition of a Projectile

The magnitude...

Question

The magnitude of vectors $\to A$ , $\to B$ and $\to C$ are $3$ , $4$ and $5$ units respectively. if $\to A + \to B = \to C$ , find the angle between $\to A$ and $\to B$ .

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Solution

$Step 1:$ $Squaring the given equation on both sides$
Let $θ$ be the angle between $\to A$ and $\to B$
$\to A + \to B = \to C$
Squaring on both sides
$(\to A + \to B)^{2} = (\to C)^{2}$
$\Rightarrow | \to A |^{2} + | \to B |^{2} + 2 \to A . \to B = | \to C |^{2}$
$\Rightarrow | \to A |^{2} + | \to B |^{2} + 2 | \to A | | \to B | cos θ = | \to C |^{2}$ $. . . . (1)$

$Step 2:$ $Calculations$
Put the values of all the variables in eq $(1)$ to get $θ$
$(3)^{2} + (4)^{2} + 2 \times 3 \times 4 cos θ = (5)^{2}$
$\Rightarrow$ $cos θ = 0$
$\Rightarrow$ $θ = 90^{\circ}$

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