Let Find a vector
which is perpendicular to both
Here
Let
Since is perpendicular to
...(1)
and ...(2)
Again ...(3)
Multiplying (1) by 7 and (2) by -2, we get,
Adding, ...(4)
Multiplying (1) by 2 and (3) by -1, we get,
Adding,
From (4),
From (1),
Let be three vectors of magnitude 5, 3, 1 respectively. If each one is perpendicular to the sum of other two vectors, prove that
If are mutually perpendicular vectors of equal magnitude, show that they are equally inclined to the vector