unit vector perpendicular to two vectors?

Question

If Vector a= 2i - 4j + k and Vector b= -4i + j +2k

Find -: a unit vector perpendicular to both vector a and b

"Sid Has" its not that simple, you try to work it out and let me know your answer.

Answer 1

A vector perpendicular to both "a" and "b" is

b×a = 9i +8j + 14k

However, this vector has a magnitude of √341 ≈ 18.4661...; clearly, not an unit vector. The unit vector you seek is thus

9i + 8j + 14k
--------------- ≈ .48738i + .43322j + .75814k
     √341

For a check, compute the sum of the squares of the above figures; it should amount to 1.

By the way, a × b is as well perpendicular to "a" and "b"; in fact, it is the same as b × a, but in the opposite direction.

Answer 2

You need to take the cross product and then normalize the magnitude of the vector.

a x b = -9i -8j -14k
The magnitude is sqrt(9^2 + 8^2 + 14^2) = sqrt(241)
So the unit vector in question is
(-9i -8j -14k)/sqrt(241)

Answer 3

Ur unit vector perp. to both above is...:
a X b,, a cross b
get the cross product of them both..

Dont tell that u can't do that !!!