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Question

A moves from a point P(1,2,3) to point Q(4,6,8). In which one of the following cases the displacement vector is same as that of A?

A
B moves from R(2,3,5) to S(1,2,3)
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B
C moves from T(7,8,5) to U(4,4,0).
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C
D moves from V(1,2,5) to W(4,6,10)
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D
E moves from X(0,0,0) to Y(1,2,3).
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Solution

The correct option is C D moves from V(1,2,5) to W(4,6,10)
The displacement vector is the difference between the final position and the initial position.
So, displacement of A is
SA=(4^i+6^j+8^k)(1^i+2^j+3^k)
=3^i+4^j+5^k
Similarly, from the options, the displacement of B,C,D and E is
SB=(1^i+2^j+3^k)(2^i+3^j+5^k)
=1^i+1^j2^k
SC=(4^i+4^j+0^k)(7^i+8^j+5^k)
=3^i4^j5^k
SD=(4^i+6^j+10^k)(1^i+2^j+5^k)
=3^i+4^j+5^k
SE=(1^i+2^j+3^k)(0^i+0^j+0^k)
=1^i+2^j+3^k
SA=SD
Hence, option (C) is correct.

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