`aa n dc` are unit vectors and `|b|=4` . The angel between `aa n dc` is `cos^(-1)(1//4)a n db-2c=lambdaadot` The value of `lambda` is `3,-4` b. `1//4,3//4` c. `-3,4` d. `-1//4,3//4`

If |veca|=3,|vecb|=4a n d the angle between aa n db is 120^@ , then find the value of |4veca+3vecb|dot

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 a. (-3)/4 b. 1/4 c. 3/4 d. 1/2

The value of 1- 1/2(3/4) + 1/3(3/4)^(2) -1/4(3/4)^(3) + ... is:

If angle theta bertween the line (x+1)/1=(y-1)/2=(z-2)/2 and the plane 2x-y+sqrt(lambda)z+4=0 is such that s intheta=1//3, the value of lambda is a. -3/5 b. 5/3 c. -4/3 d. 3/4

If vec aa n d vec b are two vectors, such that vec adot vec b<0a n d| vec adot vec b|=| vec axx vec b|, then the angle between vectors vec aa n d vec b is pi b. 7pi//4 c. pi//4 d. 3pi//4

Let Aa n dB be two events. Suppose P(A)=0. 4 ,P(B)=p ,a n dP(AuuB)=0. 7. The value of p for which Aa n dB are independent is a. 1//3 b. 1//4 c. 1//2 d. 1//5

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 a. pi//3 b. pi-cos^(-1)(1//4) c. (2pi)/3 d. cos^(-1)(1//4)

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

vec a , vec ba n d vec c are unit vectors such that | vec a+ vec b+3 vec c|=4. Angle between vec aa n d vec bi stheta_1, between vec ba n d vec c is theta_2 and between vec aa n d vec c varies [pi//6,2pi//3]dot Then the maximum of costheta_1+3costheta_2i s a. 3 b. 4 c. 2sqrt(2) d. 6

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