For any vector `vec(alpha)`, what is `(vec(alpha). hat( i)) hat(i)+(vec(alpha). hat(j)) hat(j)+(vec(alpha). hat(k)) hat(k)` equal to ?

For any vector alpha what (alpha . hat(i)) hat(i) + (alpha.hat(j)) hat(j) + (alpha.hat(k)) hat(k) equal to ?

If vec(a) . hat(i)= vec(a).(hat(i)+ hat(j)) = vec(a). ( hat(i) + hat(j) + hat(k)) =1 , then vec(a) is equal to

If vec a is any vector, show that vec a = (vec a. hat i ) hat i + (vec a. hat j) hat j + (vec a. hat k) hat k .

For any vector vec r , prove that vec r=( vec r . hat i) hat i+( vec r . hat j) hat j+( vec r . hat k) hat kdot

For any vector vec a , prove that hat i xx (vec a xx hat i)+ hat j xx (vec a xx hat j) + hat k xx(vec a xx hat k)= 2 vec a

If vec(beta) is perpendicular to both vec(alpha) and vec(gamma) where vec(alpha)= hat(k) and vec(gamma) = 2hat(i) + 3hat(j) + 4hat(k) , then what is vec(beta) equal to ?

For any vector vec r ,prove that vec r=(vec r*hat i)hat i+(vec r*hat j)hat j+(vec r*hat k)hat k

Find the angle between the vectors vec(a) and vec(b) , when (i) vec(a)=hat(i)-2hat(j)+3 hat(k) and vec(b)=3hat(i)-2hat(j)+hat(k) (ii) vec(a)=3 hat(i)+hat(j)+2hat(k) and vec(b)=2hat(i)-2hat(j)+4 hat(k) (iii) vec(a)=hat(i)-hat(j) and vec(b)=hat(j)+hat(k) .

If vec(beta) is perpendicular to both vec(alpha) and vec(lambda) where vec(alpha)=hat(k) and vec(lambda)=2hat(i)+3 hat(j)+4 hat(k) , then what is vec(beta) equal to ?