Resultant of two vectors A- and B- is of magnitude P- If B- is reversed- then resultant is of magnitude Q- What is the value of P 2 - Q 2 -

The correct option is B 2(A ^2 + B ^2 )Let θ be angle between A⃗ and B⃗ . ∴ Resultant of A⃗ and B⃗ is #160; P ...

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Byju's Answer

Standard XII

Physics

Vector Addition

Resultant of ...

Question

Resultant of two vectors $\to A$ and $\to B$ is of magnitude P. If $\to B$ is reversed, then resultant is of magnitude Q. What is the value of P $^{2}$ + Q $^{2}$ ?

2(A

^{2}

+ B

^{2}

)

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2(A

^{2}

-B

^{2}

)

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^{2}

-B

^{2}

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^{2}

+ B

^{2}

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Solution

The correct option is B 2(A $^{2}$ + B $^{2}$ )
Let $θ$ be angle between $\to A$ and $\to B$ . $∴$ Resultant of $\to A$ and $\to B$ is
$P = \sqrt{A^{2} + B^{2} + 2 A B c o s θ}$ ---(i)

When $\to B$ is reversed, then the angle between $\to A$ and - $\to B$ is (180 $^{\circ}$ - $θ$ ).Resultant of $\to A$ and - $\to B$ is

Q = $\sqrt{A^{2} + B^{2} + 2 A B c o s (180^{\circ} - θ)}$

Q = $\sqrt{A^{2} + B^{2} + 2 A B c o s θ}$ --(ii)

Squaring and adding (i) and (ii), we get $P^{2} + Q^{2} = 2 (A^{2} + B^{2})$

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Resultant of two vectors →A and →B is of magnitude P. If →B is reversed, then resultant is of magnitude Q. What is the value of P2 + Q2 ?

Resultant of two vectors $\to A$ and $\to B$ is of magnitude P. If $\to B$ is reversed, then resultant is of magnitude Q. What is the value of P $^{2}$ + Q $^{2}$ ?