If the position vectors A- B- C- and D are A - 3- - 4-5k- B-4-5-6k- C-7-9-3k- and D-4-6- then the displacement vectors AB and CD are

A=3î+4ĵ+5k̂, nbsp; B=4î+5ĵ+6k̂, nbsp; C=7î+9ĵ+3k̂, nbsp; D=4î+6ĵ nbsp; AB = B A =(4î + 5ĵ+6k̂) (3î+4ĵ+5k̂) =î+ĵ+k̂ CD = D C = (4î + 6î) (7î +9ĵ+3k ...

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Byju's Answer

Standard XI

Physics

Subtraction of a Vector

If the positi...

Question

If the position vectors $\to A, \to B, \to C, and \to D$ are $\to A = 3^i + 4^j + 5^k, \to B = 4^i + 5^j + 6^k, \to C = 7^i + 9^j + 3^k,$ and $\to D = 4^i + 6^j,$ then the displacement vectors $- - \to A B and - - \to C D$ are

Perpendicular

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Parallel

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Antiparallel

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Inclined at an angle of

60^{\circ}

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Solution

The correct option is C Antiparallel
$\to A = 3^i + 4^j + 5^k,$
$\to B = 4^i + 5^j + 6^k,$
$\to C = 7^i + 9^j + 3^k,$
$\to D = 4^i + 6^j$

$- - \to A B = \to B - \to A$
$= (4^i + 5^j + 6^k) - (3^i + 4^j + 5^k)$
$=^i +^j +^k$

$- - \to C D = \to D - \to C$
$= (4^i + 6^i) - (7^i + 9^j + 3^k)$
$= - 3^i - 3^j - 3^k$

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Similar questions

Q. If the position vectors

\to A, \to B, \to C, and \to D

are

\to A = 3^i + 4^j + 5^k, \to B = 4^i + 5^j + 6^k, \to C = 7^i + 9^j + 3^k,

and

\to D = 4^i + 6^j,

then the displacement vectors

- - \to A B and - - \to C D

are

Q. The position vectors of points

A, B, C

and

D

are

A = 3^i + 4^j + 5^k

B = 4^i + 5^j + 6^k, C = 7^i + 9^j + 3^k

and

D = 4^i + 6^j

, then the displacement vectors

- - \to A B

and

- - \to C D

are

Q. The position vectors of points

A, B, C

and

D

are

A = 3^i + 4^j + 5^k, B = 4^i + 5^j + 6^k

C = 7^i + 9^j + 3^k

and

D = 4^i + 6^j

. Then, the displacement vectors

A B

and

C D

are

Q. The position vectors of points

A, B, C

and

D

are

A = 3^i + 4^j + 5^k, B = 4^i + 5^j + 6^k

C = 7^i + 9^j + 3^k

and

D = 4^i + 6^j

. Then, the displacement vectors

A B

and

C D

are

Q. The position vectors of points

A, B, C

and

D

are

A = 3^i + 4^j + 5^k

B = 4^i + 5^j + 6^k, C = 7^i + 9^j + 3^k

and

D = 4^i + 6^j

, then the displacement vectors

- - \to A B

and

- - \to C D

are

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If the position vectors →A,→B,→C, and →D are →A=3^i+4^j+5^k, →B=4^i+5^j+6^k,→C=7^i+9^j+3^k, and →D=4^i+6^j, then the displacement vectors −−→AB and −−→CD are

The correct option is C Antiparallel →A=3^i+4^j+5^k, →B=4^i+5^j+6^k, →C=7^i+9^j+3^k, →D=4^i+6^j −−→AB=→B−→A =(4^i+5^j+6^k)−(3^i+4^j+5^k) =^i+^j+^k −−→CD=→D−→C =(4^i+6^i)−(7^i+9^j+3^k) =−3^i−3^j−3^k

If the position vectors $\to A, \to B, \to C, and \to D$ are $\to A = 3^i + 4^j + 5^k, \to B = 4^i + 5^j + 6^k, \to C = 7^i + 9^j + 3^k,$ and $\to D = 4^i + 6^j,$ then the displacement vectors $- - \to A B and - - \to C D$ are