एक बिंदु का स्थिति वेक्टर (3hati-2hatj+6hatk)m है। बल के टॉर्क का i^(th) घटक...

The position vector of a point is (3hati-2hatj+6hatk)m . The i^(th) component of torque of force (2hati+3hatj-6hatk)N acting at the point about origin in (Nm) is

Find a unit vector in the diection of the vector. (i) (3hati + 4hatj - 5hatk) , (ii) (3hati - 2hatj + 6hatk) (iii) (hati + hatk) , (iv) (2hati + hatj + 2hatk)

Find vecB xx vecA if vecA = 3hati - 2hatj + 6hatk and vecB = hati - hatj + hatk .

Find the shortest distance between the lines: (i) vec(r) = 3 hati + 8 hat(j) + 3 hatk + lambda (3 hati - hatj + hatk) and vec(r) = - 3 hat(i) - 7 hatj + 6 hatk + mu (-3 hati + 2 hatj + 4 hatk ) (ii) ( hati - hatj + 2 hatk) + lambda ( -2 hati + hatj + 3 hatk ) and (2 hati + 3 hatj - hatk) + mu (3 hati - 2 hatj + 2 hatk). (iii) vec(r) = (hati + 2 hatj + 3 hatk) + lambda ( hati - 3 hatj + 2 hatk ) and vec(r) = (4 hati + 5 hatj + 6 hatk) + mu (2 hati + 3 hatj + hatk) .

The shortest distance between the lines r = ( - hati - hatj - hatk ) + lamda ( 7 hati - 6 hatj + hatk ) and r = ( 3 hati + 5 hatj + 7 hatk ) + mu ( hati - 2 hatj + hatk )

Find the angle between the following pairs of lines : (i) vec(r) = 2 hati - 5 hatj + hatk + lambda (3 hati + 2 hatj + 6 hatk ) and vec(r) = 7 hati - 6 hatk + mu (hati + 2 hatj + 2 hatk) (ii) vec(r) = 3 hati + hatj - 2 hatk + lambda (hati - hatj - 2 hatk ) and vec(r) = 2 hati - hatj - 56 hatk + mu (3 hati - 5 hatj - 4 hatk) .

Find the position vector of the mid-point of the vector joining the points A(3hati + 2hatj + 6hatk) and B(hati + 4hatj - 2hatk)

The angle between the lines bar(r) = (2hati - 5hatj + hatk) + lamda(3hati + 2hatj + 6 hatk ) "and" bar(r) = (7hati - 6hatk) + mu(hati + 2hatj + 2hatk) is

Find the shortest distance between the lines: (i) vec(r) = 6 hat(i) + 2 hat(j) + 2 hatk + lambda (hati - 2hatj + 2 hatk) and vec(r) = - 4 hati - hatk + mu (3 hati - 2 hatj - 2 hatk ) (ii) vec(r) = (4 hat(i) - hat(j)) + lambda (hati + 2hatj - 3 hatk) and vec(r) = (hati - hatj + 2hatk) + mu (2 hati + 4 hatj - 5 hatk ) (iii) vec(r) = (hati + 2 hatj - 4 hatk) + lambda (2 hati + 3 hatj + 6 hatk ) and vec(r) = (3 hati + 3 hatj + 5 hatk) + mu (-2 hati + 3 hatj + 6 hatk )

Calculate the values of (i) hatj. (2hati - 3hatj +hatk) and (ii) (2hati - hatj) (3hati + hatk)