Question

Write the number of vectors of unit length perpendicular to both the vectors a=2i+j+2k and b=j+k

Answer 1

We know, $\bold{a\times b=|a|.|b|sin\theta(\pm n\hat)}$
Here a and b are two vectors and θ is the angle between them. and $\hat{n}$ is the unit vectors , perpendicular upon both the given vectors.

Here also it is clear that there are two possibilities of unit vectors , one are parallel { angle between unit vector and a × b is 0°} while other is antiparallel { angle between unit vector and a × b is 180° .

Hence , 2 unit vectors are perpendicular upon a = 2i + j + 2k and b = j + k

Answer 2

Answer:

We know, \bold{a\times b=|a|.|b|sin\theta(\pm n\hat)}a×b=∣a∣.∣b∣sinθ(±n

)

^

Here a and b are two vectors and θ is the angle between them. and \hat{n}

n

^

is the unit vectors , perpendicular upon both the given vectors.

Here also it is clear that there are two possibilities of unit vectors , one are parallel { angle between unit vector and a × b is 0°} while other is antiparallel { angle between unit vector and a × b is 180° .

Hence , 2 unit vectors are perpendicular upon a = 2i + j + 2k and b = j + k