Two vector each of magnitude A are inclined at angle q with each other, then magnitude of resultant vector is

The magnitude of resultant vector (R) = a 2 + b 2 + 2 a b c o s θ <!- [if gte mso 9]><xml> </xml><! [endif]->here a = b = Athen R = A 2 + A 2 + 2 A 2 c o s θ <!- [if gte mso 9]><xml> </xml><! [endif]-> = A 2 1 + c o s θ = 2 A 2 c o s 2 θ 2 = 2 A c o s θ 2 <!- [if gte mso 9]><xml> </xml><! [endif]->

Two vector each of magnitude A are inclined at angle&nbsp;q with each other, then magnitude of resultant vector is

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Physics Class 11th Physics Motion in Plane

Two vector each of magnitude A are inclined at angle q with each other, then magnitude of resultant vector is

Option 1 -

$A c o s^{2} \frac{θ}{2}$

Option 2 -

$2 A c o s \frac{θ}{2}$

Option 3 -

$2 A c o s θ$

Option 4 -

$A c o s \frac{θ}{2}$

2 Views | Posted 6 days ago

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

6 days ago

Correct Option - 2

Detailed Solution:

The magnitude of resultant vector (R)

$= \sqrt[]{a^{2} + b^{2} + 2 a b c o s θ}$

here a = b = A

then R = $\sqrt[]{A^{2} + A^{2} + 2 A^{2} c o s θ}$

$= A \sqrt[]{2} \sqrt[]{1 + c o s θ}$

$= \sqrt[]{2} A \sqrt[]{2 c o s^{2} \frac{θ}{2}}$

$= 2 A c o s \frac{θ}{2}$

The magnitude of resultant vector (R) <math> <mrow> <mo>=</mo> <mroot> <mrow> <msup> <mrow> <mi>a</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mi>b</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mi>a</mi> <mi>b</mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>θ</mi> </mrow> <mrow></mrow> </mroot> </mrow> </math>            <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1820309404"> </o:OLEObject></xml><! [endif]->here a = b = Athen R = <math> <mrow> <mroot> <mrow> <msup> <mrow> <mi>A</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mi>A</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <msup> <mrow> <mi>A</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>θ</mi> </mrow> <mrow></mrow> </mroot> </mrow> </math>  <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1820309405"> </o:OLEObject></xml><! [endif]-> <math> <mrow> <mo>=</mo> <mi>A</mi> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> <mroot> <mrow> <mn>1</mn> <mo>+</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>θ</mi> </mrow> <mrow></mrow> </mroot> </mrow> </math> <math> <mrow> <mo>=</mo> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> <mi>A</mi> <mroot> <mrow> <mn>2</mn> <mi>c</mi> <mi>o</mi> <msup> <mrow> <mi>s</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mfrac> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> </mrow> </math> <math> <mrow> <mo>=</mo> <mn>2</mn> <mi>A</mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mfrac> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math>      <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1027" DrawAspect="Content" ObjectID="_1820309406"> </o:OLEObject></xml><! [endif]->

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