Related InterviewSolutions

• Given a parallelogram `OACB`. The lengths of the vectors `vec (OA)`, `vec (OB)` & `vec (AB)` are `a`, `b` & `c` respectively. The scalar product of the vectors `vec (OC)` & `vec (OB)` is(A) `(a^2-3b^2+c^2)/2`(B) `(3a^2+b^2-c^2)/2`(C) `(3a^2-b^2+c^2)/2`(D) `(a^2+3b^2-c^2)/2`
• ABCD is a parallelogram. L is a point on BC which divides BC in the ratio `1:2`. AL intersects BD at P.M is a point on DC which divides DC in the ratio `1 : 2` and AM intersects BD in Q. Point Q divides DB in the ratioA. `1:2`B. `1:3`C. `3:1`D. `2:1`
• ABCD is a parallelogram. L is a point on BC which divides BC in the ratio `1:2`. AL intersects BD at P.M is a point on DC which divides DC in the ratio `1 : 2` and AM intersects BD in Q. `PQ : DB` is equal toA. `(2)/(3)`B. `(1)/(3)`C. `(1)/(2)`D. `(3)/(4)`
• Let `overset(to)(a),overset(to)(b),overset(to)(c )` be unit vectors such that `overset(to)(a)+overset(to)(b)+overset(to)(c ) = overset(to)(0).` Which one of the following is correct ?A. `overset(to)(a)xxoverset(to)(b)=overset(to)(b)xxoverset(to)(c)=overset(to)(c)xxoverset(to)(a)=overset(to)(0)`B. `overset(to)(a)xxoverset(to)(b)=overset(to)(b)xxoverset(to)(c)=overset(to)(c)xxoverset(to)(a)neoverset(to)(0)`C. `overset(to)(b)xxoverset(to)(b)=overset(to)(b) xx overset(to)(c) =overset(to)(a)xxoverset(to)(c)=overset(to)(0)`D. `overset(to)(a)xxoverset(to)(b),overset(to)(b)xxoverset(to)(c),overset(to)(c)xxoverset(to)(a)` are mutually perpendicular
• If `veca=hati+hatj+hatk, vecb=4hati+3hatj+4hatk and vecc=hati+alphahati+betahatk` are linearly dependent vectors and `|vecc|=sqrt3.` thenA. `alpha=1, beta =-1`B. `alpha= 1,beta =+-1`C. `alpha=- 1,beta = +-1`D. ` alpha= +- 1,beta =1`
• Let `a= 2hat(i)+ hat(j) -2hat(k) , b=hat(i) +hat(j) ` and c be a vectors such that `|c-a| =3, |(axxb)xx c|=3` and the angle between c and `axx b" is "30^(@)` . Then a. c is equal toA. `(25)/(8)`B. `2`C. `5`D. `(1)/(8)`
• Four non zero vectors willalways bea. linearly dependent b. linearly independentc. either a or b d. none of theseA. linearly dependentB. linearly independentC. either (a) or (b)D. none of these
• Let `a=3hat(i) +2hat(j)+xhat(k) " and " b=hat(i)-hat(j) +hat(k) ` for some real x Then `|axx b| =r` is possible ifA. `0 lt r le sqrt((3)/(2))`B. `sqrt((3)/(2)) lt r le 3 sqrt((3)/(2))`C. `3sqrt((3)/(2)) lt r lt 5sqrt((3)/(2))`D. `r ge 5 sqrt((3)/(2))`
• If the vectors `vec a` and `vec b`are linearly independent and satisfying `(sqrt3tantheta-1)vec a + (sqrt3sectheta-2)vec b=vec 0`,then the most general values of `theta` are:A. `npi-(pi)/(6),n inZ`B. `2npi+-(11pi)/(6)n in Z`C. `n pi+-(pi)/(6),n in Z`D. `2npi+(11pi)/(6), n in Z`
• If `overset(to)(a),overset(to)(b),overset(to)(c ),overset(to)(d)` are four distinct vectors satisfying the conditions `overset(to)(a)xxoverset(to)(b)=overset(to)(c )xx overset(to)(d) " and " overset(to)(a)xxoverset(to)(c ) = overset(to)(b)xx overset(to)(d)` then prove that `, overset(to)(a).overset(to)(b)+overset(to)(c ). overset(to)(d) ne overset(to)(a). overset(to)(c)+overset(to)(b).overset(to)(d)`.