Let ` sqrt(3i) + hatj , hati + sqrt(3j) and beta hati + (1- beta)hatj` respectively be the position vedors of the points A, B and C with respect the origin O. If the distance of C from the bisector of the acute angle between OA and OB is `(3)/(sqrt2),` then the sum all possible values of `beta` is `"_______."`

Let sqrt(3) hati + hatj , hati + sqrt(3)hatj and beta hati + (1- beta)hatj respectively be the position vedors of the points A, B and C with respect the origin O. If the distance of C from the bisector of the acute angle between OA and OB is (3)/(sqrt2), then the sum all possible values of beta is "_______."

In R^2 let sqrt(3i) + hatj , hati + sqrt(3j) and beta hati + (1- beta)hatj respectively be the position vedors of the points X, Y and Z with respect the origin O. If the distance of Z from the bisector of the acute angle between OX and OY is (3)/(sqrt2), then the possible values of beta is "_______."

Let sqrt(3)hati+hatj,hati+sqrt(3)hatj" and "betahati+(1-beta)hatj respectively be the position vectors of the points A, B and C with respect to the origin O. If distance of C from the bisector of the acute angle between OA and OB is (3)/(sqrt(2)) , then the sum of all possible values of beta is (a) 1 (b) 3 (c) 4 (c) 2

Given vec alpha=3hati+hatj+2hatk and vec beta=hati-2hatj-4hatk are the position vectors of the points A and B Then the distance of the point hati+hatj+hatk from the plane passing through B and perpendicular to AB is (a) 5 (b) 10 (c)15 (d) 20

If OA = hati +2hatj+3 hatk and OB = 4 hati +hatk are the position vectors of the points A and B then , the position vector of a point on the line passing through B and parallel to the vector OA xx OB which is at a distance of sqrt(189) units from B is

Given vec alpha=3hati+hatj+2hatk and vec beta=hati-2hatj-4hatk are the position vectors of the points A and B Then the distance of the point hati+hatj+hatk from the plane passing through B and perpendicular to AB is (a) 5 (b) 10 (c) 15 (d) 20

Given vec alpha=3hati+hatj+2hatk and vec beta=hati-2hatj-4hatk are the position vectors of the points A and B Then the distance of the point -hati+hatj+hatk from the plane passing through B and perpendicular to AB is (a) 5 (b) 10 (c) 15 (d) 20

If the position vectors of A and B are (sqrt2-1)hati-hatj and hati+(sqrt2+1)hatj respectively, then what is the magnitude of vecAB ?