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Question

A vector which makes equal angles with the vectors 13(^i2^j+2^k),15(4^i3^k),^j. is

A
5^i+^j+5^k
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B
5^i+^j+5^k
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C
5^i^j^k
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D
5^i+^j5^k
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Solution

The correct option is B 5^i+^j+5^k
Let the required vector be a=x^i+y^j+z^k. It makes equal angles with the vectors.
b=13(^i2^j2^k),c=15(4^i3^k),d=^j
a.b=a.c=a.d [b,c,d are unit vectors]
13(x2y+2z)=15(4x3z)=y
x2y+2=3y and 4x5y3z=0
x5y+2z=0 and 4x+5y+3z=0
Solving these equations, we get x= -z and x =-5y.
x5=y1=z5orx5=y1=z5
a=5^i+^j+5^k or a=5^i^j5^k

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