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Question

The dot product of a vector with vectors ^i+^j3^k, ^i+3^j2^k ,2^i+^j+4k are 0,5 and 8 respectively. Find the vector .

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Solution

Let vertor be a^i+b^j+c^k
Dot product with ^i+^j3^k=a+b3c=0 …………(1)
Dot product with ^i+3^j2^k=a+3b2c=5 ……….(2)
Dot product with 2^i+^j+4^k=2a+b+4c=8 ……………(3)
Equation (2) -Equation (1)
a+3b2cab+3c=50
2b+c=5 ………..(4)
Equation (3)-2× equation (2)
2a+b+4c2a6b+4c=810
5b+8c=2 …………..(5)
Equation (5) - 4× equation (4)
5b+8c16b8c=240
21b=42
b=4221=2
Put b=2 in (4) we get c=52b
c=52×2=54
c=1
Put b=2, c=1 in (1)
a+23×1=0
a+23=0
a1=0
(or) a=1
Hence the verctor is ^i+2^j+^k.

1257502_1326679_ans_65e63731223841178304fcbfe136c472.PNG

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