If I` vec(a)`I = 4 and `-3 le lamda le 2`,then I`lambda vec(a)`I lies in (A) [0,12] (B) [2,3] (C) [8,12] (D) [-12,8]

If |vec(a) | = 4 and -3 le lamda le 2 ,then I lambda veca I lies in (A) [0,12] (B) [2,3] (C) [8,12] (D) [-12,8]

[veci vec i vec i] = (A) 0 (B) 1 (C) vec i (D) vec k

If vec r = 3vec i + 2vec j-5vec kvec a = 2vec i-vec j + vec k, vec b = vec i + 3vec j-2vec k and vec c = -2vec i + vec j-3vec k such that vec r = lambdavec a + muvec b + deltavec c then mu, (lambda) / (2), delta are in? (A) AP (B) GP (C) HP (D) AGP

If |z-4+3i|le2 then the complex number z for which |z| is minimum is (A) 12/5+9/5i (B) 9/5-12/5i (C) 12/5-9/5i (D) -12/5+9/5i

If A=[(2,-1),(-1,2)] and i is the unit matrix of order 2, then A^2 is equal to (A) 4A-3I (B) 3A-4I (C) A-I (D) A+I

If a=7, b=5, c=3, then the value of a^2+b^2+c^2-a b-b c-c a i s -12 (b) 0 (c) 8 (d) 12

Let vec a = hat i + hat j + hat k, vec b = hat i + 4 hat j - hat k, vec c = hat i + hat j + 2 hat k and hat s be a the unit vector the magnitude of the vector (vec a .vec s)(vec b xx vec c) + (vec b. vec s)(vec c xx vec a) + ( vec c.vec s)(vec a xx vec b) is equal to (A) 1 (B) 2 (C) 3 (D) 4

Vector of length of 3 unit which is perpendicular to vec i + vec j + vec k and lies in the plane of vec i + vec j + vec k and 2vec i-3vec j, is (1) (3) / (sqrt ( 6)) (vec i-2vec j + vec k) (2) (3) / (sqrt (6)) (2vec i-vec j-vec k) (3) (3) / (sqrt (114)) ( 8vec i-7vec j-vec k) (4) (3) / (sqrt (114)) (- 7vec i + 8vec j-vec k)

vec a=2hat i+lambda_(1)hat j+3hat k,vec b=4hat i+(3-lambda_(2))hat j+6hat k and vec c=3hat i+6hat j+(lambda_(3)-1)hat k be three vectors such that vec b=2vec a and vec a is perpendicular to c then a possible value of (lambda_(1),lambda_(2),lambda_(3)) is : (a) (1,3,1)( b) (-(1)/(2),4,0)( c) (1,5,1) (d) ((1)/(2),4,-2)

If vec(a) = 2 hat(i) + 2 hat(j) + hat(k) , vec(b) = - hat(i) + hat(j) + 2 hat(k) and vec ( c) = 3 hat(i) + hat(j) such that vec(a) + lambda hat (b) is perpendicular to vec( c) , find lambda .