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Question
The number of vectors of unit length perpendicular to the vectors `vec"a" = 2hat"i" + hat"j" + 2hat"k"` and `vec"b" = hat"j" + hat"k"` is ______.
Options
One
Two
Three
Infinite
Solution
The number of vectors of unit length perpendicular to the vectors `vec"a" = 2hat"i" + hat"j" + 2hat"k"` and `vec"b" = hat"j" + hat"k"` is two.
Explanation:
The number of vectors of unit length perpendicular to vectors `vec"a"` and `vec"b"` os `vec"c"` ...(Let)
∴ `vec"c" = +-(vec"a" xx vec"b")`
So, there will be two vectors of unit length perpendicular to vectors `vec"a"` and `vec"b"`.
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