If `vec(a) = hat(i) - hat(j) + 2hat(k) , vec(b) = hat(i) +hat(j) +hat(k) ` and `vec(c ) = 2 hat(i) - hat(j) + hat(k) ` find the vector `vec (r )` satisfying the relations , ` vec(a) . vec(r ) = 1 , vec(b). vec(r ) = 2 and vec(c ) . vec (r ) = 5 `

If vec(a) = hat (i) +hat (j) , vec (b) = hat(i) - hat(j) and vec(c ) = 5 hat (i) + 2 hat (j) + 3 hat(k) , find the value of [ vec(b)vec (c ) vec(a)]

If vec (alpha ) = - hat (i) + 2 hat (j) + hat (k) , vec(b) = 3 hat(i) + hat (j) + 2 hat (k) and vec(c ) = 2 hat (i) + hat (j) + 3 hat (k) , find [ vec(c ) vec(a) vec(b)]

Let vec (a) = 2 hat (i) + hat (k) , vec (b) = hat (i) + hat (j) + hat (k) and vec (c ) = 4 hat (i) - 3 hat (j) + 7 hat (k) be three given vectors . Find a vector vec (c ) which satisfies the relations vec (r ) xx vec ( b ) = vec (c ) xx vec ( b) and vec ( r ) . vec ( a) = 0

Let vec (a) = 2 hat (i) - 2 hat (j) + hat (k) , vec (b) = hat (j) - hat (k) and vec(c ) = - hat (i) + 3 hat (j) + 2 hat (k) be three given vectors .Find sine of the angle vec(a) and vec (c )

Let vec (a) = 2 hat (i) - 2 hat (j) + hat (k) , vec (b) = hat (j) - hat (k) and vec(c ) = - hat (i) + 3 hat (j) + 2 hat (k) be three given vectors .Find angle between vec(a) and vec(b)

Let vec ( a) = hat (i) + 4 hat (j) + 2 hat (k), vec (b) = 3 hat(i) - 2 hat (j) - 7 hat (k) and vec (c ) = 2 hat (i) - hat (j) + 4 hat (k) . Find a vector vec (d) which is perpendicular to both vec (a) and vec (b) and vec ( c) . vec(d) = 18

Let vec (a) = 2 hat (i) - 2 hat (j) + hat (k) , vec (b) = hat (j) - hat (k) and vec(c ) = - hat (i) + 3 hat (j) + 2 hat (k) be three given vectors .Find vec(c ) xx (-vec(a))

Let vec (a) = 2 hat (i) - 2 hat (j) + hat (k) , vec (b) = hat (j) - hat (k) and vec(c ) = - hat (i) + 3 hat (j) + 2 hat (k) be three given vectors .Find vec(a) xx vec(b)

If vec(alpha ) = hat (i) - 2 hat (j) + 3 hat (k) , vec(beta) = 2 hat (i) - 3 hat (j) + hat(k) and vec(gamma) = 3 hat (i) + hat (j) - 2 hat (k) , find vec(alpha) . (vec(beta)xx vec (gamma)) .

If vec (a) = 2 hat (i) - 2 hat (j) + hat (k) , vec(b) = hat (i) + hat (j) - hat (k) and |vec (a) xx vec(b)| = sqrt(13 m ) then the value of m is -