The number of vectors of unit length perpendicular to vectors ` vec a=(1,1,0)a n d vec b=(0,1,1)` is a. one b. two c. three`` d. infinite

Options

A. 1
B. 2
C. 3
D. 4

Answer

B

Explanation

As given, vectors are : `vec(a)=hat(i)+hat(j)and hat(b)=hat(j)+hat(k)`
So, `vec(a)xxvec(b)` is perpendicular to `vec(a) and vec(b)`
` vec(a)xxvec(b)=|(hat(i),hat(j),hat(k)),(1,1,0),(0,1,1)|`
`=hat(i)-hat(j)+hat(k)`
and `|vec(a)xxvec(b)|=sqrt(1+1+1)=sqrt(3)`
Unit vector perpendicular to `vec(a) and vec(b)`
`=pm((vec(a)xx vec(b)))/(|vec(a)xxvec(b)|)=pm(hat(i)-hat(j)+hat(k))/(sqrt(3))`
Thus, the number of vectors perpendicular to the vectors `vec(a) and vec(b)` is 2. This is true for vectors of any length. So, it is true for vector of length 5 unit.