If the position vectors A - B - C- and D are loverrightarrow A -3 hat i -4 hat j -5 hat k - - loverrightarrow B -4 hat i -5 hat j -6 hat k - loverrightarrow C -7 hat i -9 hat j -3 hat k - l and D -4 -6 - then the displacement vectors AB and CD areA- PerpendicularB- ParallelC- Inclined at an angle of 60-D- Antiparallel

The correct option is D Antiparallel nbsp;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+5 ...

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Byju's Answer

Standard XII

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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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