Compute the magnitude of the following vectors : `a = hat(i)+hat(j)+hat(k),b=2hat(i)-7hat(j)-3hat(k),c=(1)/(sqrt(3))hat(i)+(1)/(sqrt(3))hat(j)-(1)/(sqrt(3))hat(k)`.

Explanation

Given , vector `a=hat(i) +hat(j)+hat(j)`. Comparting with `a=xhat(i)+yhat(j)+zhat(k)` we get `x=1,y=1,z=1`. The magnitude of given vector is `|vec(a)|=hat(i)+hat(j)+hat(k)=sqrt(x^2+y^2+z^2)=sqrt(1^2+1^2+2^2)=sqrt(3)` Similarly magnitude of `vec(b) =|vec(b)|=|2hat(i)-7hat(j)-3hat(k)|=sqrt(2^2+(-7)^2+(-3)^2)`
`=sqrt(4+49+9)=sqrt(62)`
and `=sqrt((2)^2+(1)^2+(-3)^2)=sqrt(4+1+9)=sqrt(14)`.
`|vec( c) |=sqrt(((1)/(sqrt(3)))^2+((1)/(sqrt(3)))^2+(-(1)/sqrt(3))^2)=sqrt((1)/(3)+(1)/(3)+(1)/(3))=1`.