The position vectors of four points A-B-C and D are- - nbsp- - nbsp-k- 2- - 5- 3-2-3k- nbsp- - 6- - nbsp-k- respectively- Then select the correct relation-AB - CDAB - 12 CDAB - 23 CDAB - 14 CD

The correct option is B AB = 12 CDA = î+ĵ+k̂ B = 2î+5ĵ C = 3î+2ĵ 3k̂ D = î+ 6ĵ k̂ AB = nbsp;B⃗ nbsp;A⃗ AB = î + 4ĵ k̂ ⇒ AB = √(1 + 16 + 1) = √(18) CD ...

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Standard XII

Physics

Comparing Vectors

The position ...

Question

The position vectors of four points A,B,C and D are $^i +^j +^k, 2^i + 5^j, 3^i + 2^j - 3^k,^i - 6^j -^k$ respectively. Then select the correct relation.

A B = C D

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A B = \frac{1}{2} C D

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A B = \frac{2}{3} C D

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A B = \frac{1}{4} C D

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Solution

The correct option is B $A B = \frac{1}{2} C D$
$\to A =^i +^j +^k$
$\to B = 2^i + 5^j$
$\to C = 3^i + 2^j - 3^k$
$\to D =^i + 6^j -^k$
$- - \to A B = \to B - \to A$
$- - \to A B =^i + 4^j -^k$
$\Rightarrow A B = \sqrt{1 + 16 + 1} = \sqrt{18}$
$- - \to C D = \to D - \to C$
$- - \to C D = - 2^i - 8^j + 2^k$
$C D = \sqrt{4 + 64 + 4} = \sqrt{72} = 2 \sqrt{18}$
$∴ A B = \frac{1}{2} C D$

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Similar questions

Q. The position vectors of four points A,B,C and D are

^i +^j +^k, 2^i + 5^j, 3^i + 2^j - 3^k,^i - 6^j -^k

respectively. Then select the correct relation.

Q. The position vector of four points

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and

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^i +^j +^k, 2^i + 5^j, 3^i + 2^j - 3^k,^i - 6^j -^k

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Then select the correct relation.

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(^i - 6^j -^k)

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The position vectors of four points A,B,C and D are^i+^j+^k,2^i+5^j,3^i+2^j−3^k,^i−6^j−^k respectively. Then select the correct relation.

The correct option is B AB=12CD→A=^i+^j+^k →B=2^i+5^j →C=3^i+2^j−3^k →D=^i+6^j−^k −−→AB=→B−→A −−→AB=^i+4^j−^k ⇒AB=√1+16+1=√18 −−→CD=→D−→C −−→CD=−2^i−8^j+2^k CD=√4+64+4=√72=2√18 ∴AB=12CD

The position vectors of four points A,B,C and D are $^i +^j +^k, 2^i + 5^j, 3^i + 2^j - 3^k,^i - 6^j -^k$ respectively. Then select the correct relation.