सदिश के मापांक ज्ञात कीजिए| vec a=hati +hatj +hatk | 12 | सदिश बीजगणित | MATHS | PRABODH PUB...

What is the value of linear velocity , "If " vec omega = 3 hati - 4 hatj + hatk and vec r = 5 hati - 6 hatj + 6 hatk ?

If vec r = 3 hati + 2 hatj - 5 hatk , vec a= 2 hati - hatj + hatk, vec b = hati + 3 hatj - 2hatk and vec c=2 hati + hatj - 3 hatk " such that " hat r = x vec a +y vec b + z vec c then

If veca = 3hati - hatj - 4hatk , vecb = -2hati + 4hatj - 3hatk and vec c = hati + 2hatj - hatk then |3veca - 2vec b + 4vec c | is equal to

Consider the equations of the straight lines given by : L_(1) : vec(r) = (hati + 2 hatj + hatk ) + lambda ( hati - hatj + hatk) L_(2) : vec(r) = (2 hati - hatj - hatk) + mu ( 2 hati + hatj + 2 hatk) . If vec(a_(1))= hati + 2 hatj + hatk, " " vec(b_(1)) = hati - hatj + hatk , vec(a_(2)) = 2 hat(i) - hatj - hatk, vec(b_(2)) = 2 hati + hatj + 2 hatk , then find : (i) vec(a_(2)) - vec(a_(1)) " " (ii) vec(b_(2)) - vec(b_(1)) (iii) vec(b_(1))xx vec(b_(2)) " " (iv) vec(a_(1)) xx vec(a_(2)) (v) (vec(b_(1)) xx vec(b_(2))).(vec(a_(1)) xxvec(a_(2))) (vi) the shortest distance between L_(1) and L_(2) .

What is the projection of vec(A) = hati + hatj+ hatk on vec(B) = (hati + 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) .

If vector vec a = hati + hatj + hatk , vecb = 4 hati + 3 hatj + 4 hatk and vec c = hati + alpha hatj + beta hatk are linearly dependent and | vec c | = sqrt3 , then value of | alpha | + | beta | is

Angle between the planes: (i) vec(r). (hati - 2 hatj - hatk) = 1 and vec(r). (3 hati - 6 hatj + 2 hatk) = 0 (ii) vec(r). (2 hati + 2 hatj - 3 hatk ) = 5 and vec(r) . ( 3 hati - 3 hatj + 5 hatk ) = 3

Show that the lines : vec(r) = 3 hati + 2 hatj - 4 hatk + lambda (hati + 2 hatj + 2 hatk) and vec(r) = 5 hati - 2 hatj + mu (3 hati + 2 hatj + 6 hatk) (ii) vec(r) = (hati + hatj - hatk) + lambda (3 hati - hatj) . and vec(r) = (4 hati - hatk) + mu (2 hati + 3 hatk) are intersecting. Hence, find their point of intersection.