If $\vec{A} a n d \vec{B}$ are two vectors satisfying the relation $\vec{A} . \vec{B} = | \vec{A} \times \vec{B} | .$ Then the value of $| \vec{A} - \vec{B} |$ will be:

Option 1 -

$\sqrt[]{A^{2} + B^{2} - \sqrt[]{2} A B}$

Option 2 -

$\sqrt[]{A^{2} + B^{2}}$

Option 3 -

$\sqrt[]{A^{2} + B^{2} + 2 A B}$

Option 4 -

$\sqrt[]{A^{2} + B^{2} + 2 A B}$

Option 5 -

$\sqrt[]{A^{2} + B^{2} + \sqrt[]{2} A B}$

3 Views | Posted a month ago

Asked by Shiksha User

1 Answer

Answered by

alok kumar singh | Contributor-Level 10

a month ago

Correct Option - 2

Detailed Solution:

$\vec{A} . \vec{B} = | \vec{A} \times \vec{B} | \Rightarrow A B c o s θ = A B s i n θ \Rightarrow θ = 45 °$

$| \vec{A} - \vec{B} | = \sqrt[]{A^{2} + B^{2} - 2 A B c o s θ} = \sqrt[]{A^{2} + B^{2} - 2 A B \times \frac{1}{\sqrt[]{2}}} = \sqrt[]{A^{2} + B^{2} - \sqrt[]{2} A B}$

<!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1816090638"> </o:OLEObject></xml><! [endif]-> <math> <mrow> <mover accent="true"> <mi>A</mi> <mo>→</mo> </mover> <mo>.</mo> <mover accent="true"> <mi>B</mi> <mo>→</mo> </mover> <mo>=</mo> <mrow> <mo>|</mo> <mrow> <mover accent="true"> <mi>A</mi> <mo>→</mo> </mover> <mo>×</mo> <mover accent="true"> <mi>B</mi> <mo>→</mo> </mover> </mrow> <mo>|</mo> </mrow> <mo>⇒</mo> <mi>A</mi> <mtext> </mtext> <mtext> </mtext> <mi>B</mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>θ</mi> <mo>=</mo> <mi>A</mi> <mtext> </mtext> <mtext> </mtext> <mi>B</mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>θ</mi> <mo>⇒</mo> <mi>θ</mi> <mo>=</mo> <mn>4</mn> <mn>5</mn> <mo>°</mo> </mrow> </math>              <math> <mrow> <mrow> <mo>|</mo> <mrow> <mover accent="true"> <mi>A</mi> <mo>→</mo> </mover> <mo>−</mo> <mover accent="true"> <mi>B</mi> <mo>→</mo> </mover> </mrow> <mo>|</mo> </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> <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> <mo>×</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> <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> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> <mi>A</mi> <mi>B</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="_1816090639"> </o:OLEObject></xml><! [endif]->

0 Upvotes 0 Downvotes

Get authentic answers from experts, students and alumni that you won't find anywhere else

On Shiksha, get access to

65k Colleges
1.2k Exams
688k Reviews
1800k Answers

Community GuidelinesUser Points System

QuestionsDiscussionsTags

If $\vec{A} a n d \vec{B}$ are two vectors satisfying the relation $\vec{A} . \vec{B} = | \vec{A} \times \vec{B} | .$ Then the value of $| \vec{A} - \vec{B} |$ will be:

1 Answer

Learn more about...

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question

If A → a n d B → are two vectors satisfying the relation A → . B → = | A → × B → | . Then the value of | A → − B → | will be:

1 Answer

Learn more about...

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question

If $\vec{A} a n d \vec{B}$ are two vectors satisfying the relation $\vec{A} . \vec{B} = | \vec{A} \times \vec{B} | .$ Then the value of $| \vec{A} - \vec{B} |$ will be: