If `a \ "a n d" \ c` are unit vectors and `|b|=4` . The angle between `a` and `c` is `cos^(-1)(1//4)` and `a xx b=2a xx c` then, `b-2c=lambdaadot` The value of `lambda` is

Let A,B,C be three unit vectors and A.B= A.C=0. If the angle between B and C is pi/6 , then A is equals to

If vec a , vec b , vec c are non-coplanar vector and lambda is a real number, then the vectors vec a+2 vec b+3 vec c ,lambda vec b+mu vec ca n d(2lambda-1) vec c are coplanar when a. mu in R b. lambda=1/2 c. lambda=0 d. no value of lambda

The value of cos(1/2cos^(-1)(1/8)) is (a) 3/4 (b) -3/4 (c) 1/(16) (d) 1/4

If vec aa n d vec b are two unit vectors incline at angle pi//3 , then { vec axx( vec b+ vec axx vec b)}dot vec b is equal to (-3)/4 b. 1/4 c. 3/4 d. 1/2

If hat a , hat b ,a n d hat c are three unit vectors, such that hat a+ hat b+ hat c is also a unit vector and theta_1,theta_2 and theta_3 are angles between the vectors hat a , hat b ; hat b , hat ca n d hat c , hat a respectively, then among theta_1,theta_2 and theta_3 . a. all are acute angles b. all are right angles c. at least one is obtuse angle d. none of these

Let vec a , vec b ,a n d vec c be non-zero vectors and vec V_1= vec axx( vec bxx vec c)a n d vec V_2=( vec axx vec b)xx vec c. Vectors vec V_1a n d vec V_2 are equal. Then (a). vec aa n vec b are orthogonal (b). vec aa n d vec c are collinear (c). vec ba n d vec c are orthogonal (d). vec b=lambda( vec axx vec c)w h e nlambda is a scalar

The position vectors of the vertices A ,Ba n dC of a triangle are three unit vectors vec a , vec b ,a n d vec c , respectively. A vector vec d is such that vec d ⋅ vec a = vec d ⋅ vec b = vec d ⋅ vec c a n d vec d=lambda( vec b+ vec c)dot Then triangle A B C is a. acute angled b. obtuse angled c. right angled d. none of these

If a ,b and c are in A.P. and b-a ,c-b and a are in G.P., then a : b : c is (a). 1:2:3 (b). 1:3:5 (c). 2:3:4 (d). 1:2:4

If a , ba n dc are the side of a triangle, then the minimum value of (2a)/(b+c-a)+(2b)/(c+a-b)+(2c)/(a+b-c)i s (a) 3 (b) 9 (c) 6 (d) 1

If ( vec axx vec b)xx( vec bxx vec c)= vec b ,w h e r e vec a , vec b ,a n d vec c are nonzero vectors, then 1. vec a , vec b ,a n d vec c can be coplanar 2. vec a , vec b ,a n d vec c must be coplanar 3. vec a , vec b ,a n d vec c cannot be coplanar 4.none of these