यदि विद्युत क्षेत्र `(6 hat(i) + 4 hat(j) + 4 hat(k))` द्वारा दिया गया है, तो विद्युत प्रवाह की गणना करें

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) .

Write the value of [ hat i- hat j\ hat j- hat k\ hat k- hat i]

Find the vector and cartesan equation of the plane passing through the poin (1,2,-4) and parallel to the lines. vec(r ) = hat(i) + 2 hat(j) - 4 hat(k) + lambda (2 hat(i) + 3 hat(j) + 6 hat(k)) and vec(r) = hat(i) - 3 hat(j) + 5 hat(k) + mu (hat(i) + hat(j) - hat(k)) .

Prove that [hat(i)hat(j)hat(k)]=1, and [hat(i)hat(k)hat(j)]=-1 .

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))

Given two vectors A = -4hat(i) + 4hat(j) + 2hat(k) and B = 2hat(i) - hat(j) - hat(k) . The angle made by (A+B) with hat(i) + 2hat(j) - 4hat(k) is :

If the vectors 2 hat(i) - q hat(j) + 3 hat(k) and 4 hat(i) - 5 hat(j) + 6 hat(k) are collinear then find the value of q.

Find the unit vectors perpendicular to the plane of the vectors vec(a) = 2 hat(i) - 6 hat(j)- 3 hat(k) and vec(b)= 4 hat(i) + 3 hat(j) - hat(k).

Find the angle between hat(i)+hat(j)+hat(k) and hat(i)+hat(j)-hat(k) .