If `bar(a) = 4 hat(i) + 3 hat(k) and bar(b) = - 2 hat(i) + hat(j) + 5 hat(k)` then find `2 bar(a) + 5 bar(b)`

Find bar(a). bar(b) xx bar(c) , if bar(a) = 3 hat(i) - hat(j) + 4 hat(k), bar(b) = 2hat(i) + 3 hat(j) - hat(k), bar(c) = - 5 hat(i) + 2 hat(j) + 3 hat(k)

If vec(a) = 5 hat(i) - hat(j) - 3 hat(k) and vec(b) = hat(i) + 3 hat(j) - 5 hat(k) , find the angle between vec(a) and vec(b) .

Show that the following points whose position vectors are given are collinear : (i) 5 hat(i) + 5 hat(k), 2 hat(i) + hat(j) + 3 hat(k) and - 4 hat(i) + 3 hat(j) - hat(k) (ii) - 2 hat(i) + 3 hat(j) + 5 hat(k), hat(i) + 2 hat(j) + 3 hat(k) and 7 hat(i) - hat(k) .

If vec(a) = hat(i) + hat(j) + 2 hat(k) and vec(b) = 3 hat(i) + 2 hat(j) - hat(k) , find the value of (vec(a) + 3 vec(b)) . ( 2 vec(a) - vec(b)) .

Let bar(alpha) = 3hat(i) + hat(j) " and " bar(beta)=2hat(i) -hat(j)+3hat(k). "if "bar(beta)=bar(beta)_(1)-bar(beta)_(2) where bar(beta)_(1) is parallel to bar(alpha) and bar(beta)_(2) perpendicular to bar(alpha) then bar(beta)_(1)xx bar(beta)_(2) is equal to

If bar(a)=3hat(i)-2hat(j)+7hat(k),bar(b)=5hat(i)+hat(j)-2hat(k)andbar(c)=hat(i)+hat(j)-hat(k) , then find bar(a)*(bar(b)xxbar(c)) .

Consider the vectors bar(a)=hat(i)-2hat(j)+hat(k) and bar(b)=4hat(i)-4hat(j)+7hat(k) . What is the scalar projection of bar (a) on bar( b) ?

If bar(a)=(1)/(sqrt(10))(3hat(i)+hat(k)) and bar(b)=(1)/(7)(2hat(i)+3hat(j)-6hat(k)) then the value of (2bar(a)-bar(b)*((bar(a)timesbar(b))times(bar(a)+2bar(b))} is equal to

The position vectors of points A, B , C and D are vec(A) = 3hat(i) + 4hat(j) + 5hat(k), vec(B) = 4hat(i)+5hat(j) + 6hat(k), vec(C )= 7hat(i) + 9hat(j) + 3hat(k) and vec(D) = 4hat(i) + 6hat(j) then the displacement vectors bar(AB) and bar(CD) are :

Find the area of the parallelogram whose adjacent sides are represented by the vectors (i) vec(a)=hat(i) + 2 hat(j)+ 3 hat(k) and vec(b)=-3 hat(i)- 2 hat(j) + hat(k) (ii) vec(a)=(3 hat(i)+hat(j) + 4 hat(k)) and vec(b)= ( hat(i)- hat(j) + hat(k)) (iii) vec(a) = 2 hat(i)+ hat(j) +3 hat(k) and vec(b)= hat(i)-hat(j) (iv) vec(b)= 2 hat(i) and vec(b) = 3 hat(j).