Motion in a Plane Physics NCERT Exemplar Solutions Class 12th Chapter Four Class 12th Physics Physics NCERT Exemplar Solutions Class 11th Chapter Five

Two vectors $\vec{A} a n d \vec{B}$ have equal magnitudes. If magnitude of $\vec{A} + \vec{B}$ is equal to two times the magnitude of $\vec{A} - \vec{B},$ then the angle between $\vec{A} a n d \vec{B}$ will be:

Option 1 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>s</mi> <mi>i</mi> <msup> <mrow> <mi>n</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>3</mn> </mrow> <mrow> <mn>5</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> </math> </span></p>

Option 2 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>s</mi> <mi>i</mi> <msup> <mrow> <mi>n</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>3</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> </math> </span></p>

Option 3 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>c</mi> <mi>o</mi> <msup> <mrow> <mi>s</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>3</mn> </mrow> <mrow> <mn>5</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> </math> </span></p>

Option 4 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>c</mi> <mi>o</mi> <msup> <mrow> <mi>s</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>3</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> </math> </span></p>

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Alok Kumar Singh | Contributor-Level 10

6 months ago

Correct Option - 3

Detailed Solution:

$| \vec{A} + \vec{B} | = 2 | \vec{A} - \vec{B} |$

Given A = B

Squaring equation (1) both side.

${| \vec{A} + \vec{B} |}^{2} = {(2 | \vec{A} - \vec{B} |)}^{2}$

$A^{2} + B^{2} + 2 \vec{A} . \vec{B} = 4 (A^{2} + B^{2} - 2 \vec{A} . \vec{B})$

2A² + 2A² cosq = 4 (2A² – 2A² cosq)

2A² + 2A² cosq = 8A² – 8A² cosq

10A² cosq = 6A²

cosq = $\frac{3}{5}$

q = cos^-1 (3/5)

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Physics NCERT Exemplar Solutions Class 12th Chapter Four 2025

Physics NCERT Exemplar Solutions Class 12th Chapter Four 2025

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