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Question

A = 3 ^i + 4 ^j and B = 5 ^i + 2 ^j. What is unit vector along the direction of AB ?
  1. 45 ^i + 35 ^j
  2. 35 ^i + 45 ^j
  3. 54 ^i + 35 ^j
  4. 45 ^i + 53 ^j


Solution

The correct option is A 45 ^i + 35 ^j
Given:
A = 3 ^i + 4 ^j
B = 5 ^i + 2 ^j
Then,  AB 
= (3 ^i + 4 ^j) + (5 ^i + 2 ^j)
= 8 ^i + 6 ^j

unit vector along AB
= A+B|A+B|
= 8^i+6^j(8)2+(6)2
= 810 ^i + 610 ^j
45 ^i + 35 ^j

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