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Question

Unit orthogonal vector to the vector (3,4) is ______.

A
(35,45)
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B
(45,35)
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C
(45,35)
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D
(35,45)
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Solution

The correct option is A (45,35)
Let ¯¯¯y=(a,b) is unit orthogonal vector to ¯¯¯x=(3,4)
¯¯¯y=(a,b) unit vector ¯¯¯y=1
a2+b2=1
a2+b2=1...(1)
Now ¯¯¯x¯¯¯y
¯¯¯x¯¯¯y=0
(3,4).(a,b)=0
3a+4b=0
a=43b...(2)
Now subtitute value of (2) in (1)
169b2+b2=1
16b2+b2=1
25b2=9
b2=925
b=±35
If b=35 then from (2) we get
a=45
Required vector (a,b)=(45,35)
And if b=35 then from (2) we get
a=45
Required vector is (45,35)
Here ¯¯¯y=(45,35)

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