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Question
Given →A=2^i+3^j and →B=^i+^j. The component of vector →A perpendicular to vector →B and in the same plane as →B is
Given →A=2^i+3^j and →B=^i+^j. The component of vector →A perpendicular to vector →B and in the same plane as →B is
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Solution
The correct option is D 1√2(^j−^i)
We know, (→i+→j)(→i−→j)=0
Vector (→i−→j) is perpendicular to →B.
Let, (→i−→j) = →C
Now, (→A.→C)=(2→i+3→j)(→i−→j)
The required component is:
(→A.→C)→CC=2→i+3→j)(→i−→j)(→i−→j)∣∣→i−→j∣∣
(→A.→C)→CC=−1√2(→i−→j).......(since, C=√(1+1)=√2)
(→A.→C)→CC=1√2(→j−→i)
We know, (→i+→j)(→i−→j)=0
Vector (→i−→j) is perpendicular to →B.
Let, (→i−→j) = →C
Now, (→A.→C)=(2→i+3→j)(→i−→j)
The required component is:
(→A.→C)→CC=2→i+3→j)(→i−→j)(→i−→j)∣∣→i−→j∣∣
(→A.→C)→CC=2→i+3→j)(→i−→j)(→i−→j)∣∣→i−→j∣∣
(→A.→C)→CC=−1√2(→i−→j).......(since, C=√(1+1)=√2)
(→A.→C)→CC=1√2(→j−→i)
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