The position vector of four points A- B- C and D are - -k- 2- 5- 3- 2- 3k- -6- - k- Then select the correct relation-

A = î+ ĵ+ k̂ B = 2 î+ 5ĵ C = 3î+ 2ĵ 3 k̂ D = î 6ĵ k̂ AB = B A AB = î+ 4ĵ k̂ ⇒ AB = √(1+16+1) = √(18) CD = D C CD = 2î 8ĵ+2 k̂ CD = √(4+64+4) = √(72) = 2 ...

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Byju's Answer

Standard XI

Physics

Addition and Subtraction in Unit Vector Notation

The position ...

Question

The position vector of four points $A, B, C$ and $D$ are $^i +^j +^k, 2^i + 5^j, 3^i + 2^j - 3^k,^i - 6^j -^k$ .
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 vector 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

.
Then select the correct relation.

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. Let

(^i +^j +^k), (2^i + 5^j), (3^i + 2^j - 3^k)

and

(^i - 6^j -^k)

be the position vectors of points of points

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respectively. Then show that

A B ∥ C D

Q. If

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

and

^i - 6^j -^k

are the position vectors of points

A, B, C

and

D

respectively, then find the angle between

\to A B

and

\to C D

Q. Th position vector 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

.
Then select the correct relation.

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