If the angle between the vectors `bar a` and `bar b` having direction ratios 1, 2, 1 and 1, 3k, 1 is `(pi)/(4)`, then k =

If the angles between the vector bara and barb having directio ratios 1, 2,1 and 1, 3k ,1 is (pi)/(4) , find k.

The angle between the vectors a and b having direction ratios (-p,1,-2) and (2,-p,-1) is pi/3 then the value of p is

If the angle between the lines with direction ratios 2, -1, 1 and 1, k, 2 is 60^(@) , then k =

If the cosine of the angle between the lines with direction ratios 1, -1, 2 and 0, 1, k is (sqrt(3))/(2) , then k =

The acute angle between the vectors bar(AB) and bar(CD) , where A-=(1,2-1), B-=(2, 1,1), C-=(2, 1, -2), D-=(3, 2,1) is

If the vector bar(i)-bar(j)+bar(k) bisects the angle between the vector bar(a) and the vector 4bar(i)+3bar(j) , then the unit vector in the direction of bar(a) is (xbar(i)+ybar(j)+zbar(k)) then x-15y+5z is equal to

If the vector -bar(i)+bar(j)-bar(k) bisects the angles between the vector bar(c) and the vector 3bar(i)+4bar(j) , then the unit vector in the direction of bar(c) is

If the vector -bar(i)+bar(j)-bar(k) bisects the angles between the vector bar(c) and the vector 3bar(i)+4bar(j) ,then the unit vector in the direction of bar(c) is

If angle between bar(a) and bar( b) is (pi)/(3) then angle. Between 2bar( a) and -3bar(b) is. (A) (pi)/(3) (B) (2 pi)/(3) (C) (pi)/(6) (D) (5 pi)/(3)

Let bar(a) , bar(b) and bar(c) be non-zero vectors such that (bar(a)timesbar(b))timesbar(c)=(1)/(3)|bar(b)||bar(c)|bar(a) ..If theta is the acute angle between the vectors bar(b) and bar(c) then sin theta=2k then k=