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 - A- 2 A 2- B 2B- A2-B2C- 2 A 2- B 2D- A2-B2

The correct option is A 2(A^2 + B^2)Let θ be angle between A⃗ and B⃗ ∴ Resultant of A⃗ and B⃗ is P=√(A^2+B^2+2AB cos θ) ...(i) When B⃗ is reversed, th ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Acceleration in 2D

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})

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

2 (A^{2} - B^{2})

No worries! We‘ve got your back. Try BYJU‘S free classes today!

A^{2} - B^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

A^{2} + B^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $2 (A^{2} + B^{2})$
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
$P^{2} + Q^{2} = 2 (A^{2} + B^{2})$

Suggest Corrections

Similar questions

Q. 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}

The maximum value of the expression $y = 2 (a - x) (x + \sqrt{x^{2} + b^{2}})$ is

Q. If a cot θ + b cosec θ = p and b cot θ − a cosec θ = q, then p² − q² =

(a) a²− b²
(b) b² − a²
(c) a² + b²
(d) b − a

If $u = \sqrt{a^{2} c o s^{2} θ + b^{2} s i n^{2} θ} + \sqrt{a^{2} s i n^{2} θ + b^{2} c o s^{2} θ}$ , then the difference between the maximum and minimum values of $u^{2}$ is given by

Q. The resultant of two vectors

\to A

and

\to B

is perpendicular to the vector

\to A

and its magnitude is equal to half of the magnitude of

\to B

figure. The angle between

\to A

and

\to B

Join BYJU'S Learning Program

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 $P^{2} + Q^{2}$ ?