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Question

# What is the unit vector parallel to a=3i+4j−2k?.What vector should be added to a so that resultant is the unit vector →i?

A
1(29)(3i4j+2k)b=+2i4j2k.
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B
1(29)(3i+4j+2k),b=2i+4j+2k.
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C
1(29)(3i+4j2k),b=2i4j+2k.
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D
1(29)(3i4j+2k),b=2i+4j+2k.
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Solution

## The correct option is B 1√(29)(3i+4j−2k),b=−2i−4j+2k.We have a a=3i+4j−2k∴|a|=√9+16+4=√29∴ the unit vector parallel to a =a|a|=1√(29)(3i+4j−2k).Now suppose b is the vector which when added to a gives the resultant i.Then a+b=ior b=i−a=i−(3i+4j−2k) ∴b=−2i−4j+2k.

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