सदिशों `2hat(i) -hat(j) + 2hat(k)` और `3hat(i) + 3hat(j) + 4hat(k)` के बीच का कोण ज्ञात कीजिये।

Vector vec(A)=hat(i)+hat(j)-2hat(k) and vec(B)=3hat(i)+3hat(j)-6hat(k) are :

The two vectors A=2hat(i)+hat(j)+3hat(k) and B=7hat(i)-5hat(j)-3hat(k) are :-

Find the shortest distance between the lines : vec(r) = (4hat(i) - hat(j)) + lambda(hat(i) + 2hat(j) - 3hat(k)) and vec(r) = (hat(i) - hat(j) + 2hat(k)) + mu (2hat(i) + 4hat(j) - 5hat(k))

The position vectors of three points A,B anc C (-4hat(i) +2hat(j) -3hat(k)) (hat(i) +3hat(j) -2hat(k)) "and " (-9hat(i) +hat(j) -4hat(k)) respectively . Show that the points A,B and C are collinear.

Find ( vec (a) xxvec (b)) and |vec(a) xx vec (b)| ,when (i) vec(a) = hat(i)-hat(j)+ 2hat(k) and vec(b)= 2 hat(i)+3 hat(j)-4hat(k) (ii) vec(a)= 2hat (i)+hat(j)+ 3hat(k) and vec(b)= 3hat(i)+5 hat(j) - 2 hat(k) (iii) vec(a)=hat(i)- 7 hat(j)+ 7hat(k) and vec(b) = 3 hat(i)-2hat(j)+2 hat(k) (iv) vec(a)= 4hat(i)+ hat(j)- 2hat(k) and vec(b) = 3 hat(i)+hat(k) (v) vec(a) = 3 hat(i) + 4 hat(j) and vec(b) = hat(i)+hat(j)+hat(k)

Projection of the vector 2hat(i) + 3hat(j) + 2hat(k) on the vector hat(i) - 2hat(j) + 3hat(k) is :

If vector hat(i)+hat(j)+hat(k), hat(i)-hat(j)+hat(k) and 2hat(i)+3hat(j)+lambda hat(k) are coplanar, then lambda is equal to