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

If A(-2,1),B(2,3)a n dC(-2,-4) are three points, find the angle between B Aa n dB Cdot

If A(-2,1),B(2,3)a n dC(-2,-4) are three points, find the angle between B Aa n dB Cdot

If the angel between unit vectors vec aa n d vec b60^0 , then find the value of | vec a- vec b|dot

If vec a and vec b are unequal unit vectors such that ( vec a- vec b)xx[( vec b+ vec a)xx(2 vec a+ vec b)]= vec a+ vec b , then angle theta between vec aa n d vec b is 0 b. pi//2 c. pi//4 d. pi

If vec aa n d vec b are any two vectors of magnitudes 1 and 2, respectively, and (1-3 vec adot vec b)^2+|2 vec a+ vec b+3( vec axx vec b)|^2=47 , then the angel between vec aa n d vec b is pi//3 b. pi-cos^(-1)(1//4) c. (2pi)/3 d. cos^(-1)(1//4)

If a ,b , a n dc are in G.P. and x ,y , respectively, are the arithmetic means between a ,b ,a n db ,c , then the value of a/x+c/y is 1 b. 2 c. 1//2 d. none of these

If a ,b , a n dc are in G.P. and x ,y , respectively, are the arithmetic means between a ,b ,a n db ,c , then the value of a/x+c/y is 1 b. 2 c. 1//2 d. none of these

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

Statement 1: If vec ua n d vec v are unit vectors inclined at an angle alphaa n d vec x is a unit vector bisecting the angle between them, then vec x=( vec u+ vec v)//(2sin(alpha//2)dot Statement 2: If "Delta"A B C is an isosceles triangle with A B=A C=1, then the vector representing the bisector of angel A is given by vec A D=( vec A B+ vec A C)//2.

In a quadrilateral A B C D , vec A C is the bisector of vec A Ba n d vec A D , angle between vec A Ba n d vec A D is 2pi//3 , 15| vec A C|=3| vec A B|=5| vec A D|dot Then the angle between vec B Aa n d vec C D is cos^(-1)(sqrt(14))/(7sqrt(2)) b. cos^(-1)(sqrt(21))/(7sqrt(3)) c. cos^(-1)2/(sqrt(7)) d. cos^(-1)(2sqrt(7))/(14)