Question

# Match List I with the List II and select the correct answer using the code given below the lists : List IList II(A)The possible value of a if →r=(^i+^j)+λ(^i+2^j−^k)(P) −4and →r=(^i+2^j)+μ(−^i+^j+a^k) are not consistent,where λ and μ are scalars, is(B)The angle between vectors →a=λ^i−3^j−^k and(Q) −2→b=2λ^i+λ^j−^k is acute, whereas vector →bmakes an obtuse angle with the axes of coordinates.Then λ can be(C)The possible value of a such that 2^i−^j+^k,(R)    1^i+2^j+(1+a)^k and 3^i+a^j+5^k are coplanar, is(D)If →A=2^i+λ^j+3^k,→B=2^i+λ^j+^k,→C=3^i+^j(S)    2and →A+λ→B is perpendicular to →C,then |2λ| is(T)    3   Which of the following is the only CORRECT combination?(A)→(P),(Q),(R) (A)→(P),(Q),(S),(T)(B)→(P),(S)(B)→(S),(T)

Solution

## The correct option is B (A)→(P),(Q),(S),(T)(A) Given equations are consistent if (^i+^j)+λ(^i+2^j−^k)=(^i+2^j)+μ(−^i+^j+a^k) ⇒1+λ=1−μ, 1+2λ=2+μ, −λ=aμ ⇒λ=13 and μ=−13 ⇒a=1 So, for inconsistency, a≠1 (A)→(P),(Q),(S),(T) (B) →a=λ^i−3^j−^k  →b=2λ^i+λ^j−^k Angle between →a and →b is acute. ∴→a⋅→b>0 ⇒2λ2−3λ+1>0 ⇒(2λ−1)(λ−1)>0 ⇒λ∈(−∞,12)∪(1,∞) Also, →b makes an obtuse angle with the axes. Therefore, →b.^i<0⇒λ<0 →b.^j<0⇒λ<0 Hence, λ can be −4,−2 (B)→(P),(Q)

Suggest corrections