A Show that equation of angle bisectors of line `vec r=a+lambda vec b and vec r =vec b + mu vec a` are `vec r = (vec a+vec b) + gamma(|vec b| vec a ±|vec a|vec b)`

Write the equation of the plane containing the lines vec r= vec a+lambda vec b\ a n d\ vec r= vec a+mu vec c

Write the equation of the plane containing the lines vec r= vec a+lambda vec b\ a n d\ vec r= vec a+mu vec c

Let lambda = vec a xx (vec b + vec c), vec mu = vec b xx (vec c + vec a) and vec nu = vec c xx (vec a + vec b). Then

[vec a + vec b, vec b + vec r * vec cvec c + vec a] = 2 [vec with bvec c]

If vec a is a unit vector, vec a xxvec r = vec b, vec a * vec r = c, vec a * vec b = 0 then vec r is equal to

If vec a is a unit vector, vec a xxvec r = vec b, vec a * vec r = c, vec a * vec b = 0, then vec r is equal to

If vec a + vec b = vec c and | vec a | = | vec b | = | vec c | find the angle between vec a and vec b

If vec a and vec b are orthogonal unit vectors, then for a vector vec r noncoplanar with vec a and vec b , vector rxxa is equal to a. [ vec r vec a vec b] vec b-( vec r. vec b)( vec bxx vec a) b. [ vec r vec a vec b]( vec a+ vec b) c. [ vec r vec a vec b] vec a-( vec r. vec a) vec axx vec b d. none of these

If vec a and vec b are orthogonal unit vectors, then for a vector vec r noncoplanar with vec a and vec b , vector rxxa is equal to a. [ vec r vec a vec b] vec b-( vec r. vec b)( vec bxx vec a) b. [ vec r vec a vec b]( vec a+ vec b) c. [ vec r vec a vec b] vec a-( vec r. vec a) vec axx vec b d. none of these

A vector equation of the line of intersection of the planes vec r = vec b + lambda_ (1) (vec b-vec a) + mu_ (1) (vec a + vec c) vec r = vec c + lambda_ (2) (vec b-vec c) + mu_ (2) (vec a + vec b) and vec a, vec b, vec c being non coplanar vectors is