Question
Dot product of a vector with vectors 
are respectively 9, 7 and 6. Find the vector.
Solution
Let 
be required vector.
From given conditions,
...(1)
...(2)
...(3)
Multiplying (1) by 7 and (3) by 1, we get,
14x + 21 y + 7z = 63
x – 3y – 7z = 6
Adding, we get.
15x +18y = 69 or 5x + 6y = 23 …(4)
Multiplying (2) by 6 and (4) by 1, we get,
24x + 6y = 42 ...(5)
5x + 6y = 23 ...(6)
Subtracting (6) from (5), we get,
19x = 19 or x = 1
Putting x = 1 in (2), we get,
4 + y = 7 or y = 3
Putting x = 1, y = 3 in (1), we get,
2 + 9 + z = 9 or z = – 2
