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Question

Find the shortest distance between ¯r=^i+λ(^j+^k)and ¯r= 2^j+β(2^k).


A
1
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B
2
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C
3
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D
4
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Solution

The correct option is C 1
As we know shortest distance between ¯r=¯a+λ¯p and ¯r= ¯b+β¯q is (¯a¯b).(¯pׯq)(|¯pׯq|) Lets substitute.
Here, for ¯a and ¯b we have ^i and 2^j.
¯p=^j+^k,   ¯q=2^k(¯a¯b).(¯pׯq)=(^i2^j).(¯pׯq)¯pׯq=∣ ∣ ∣^i^j^k011002∣ ∣ ∣=^i(2)(^i2^i).(2^i)=22¯pׯq=22=1 units.

Mathematics

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