Let a=i+2j+k and b=2i+7j+3k. Let L_1 :r=(-i+2j+k)+ a , ∈R and L_2 :r (j+k )+ b , ∈R be two lines. If the line L_3 passes through the point of intersection of L_1 and L_2, and is parallel to a+b, then…

Question

Let a=i+2j+k and b=2i+7j+3k. Let L_1 :r=(-i+2j+k)+ a , ∈R and L_2 :r (j+k )+ b , ∈R be two lines. If the line L_3 passes through the point of intersection of L_1 and L_2, and is parallel to a+b, then L_3 passes through the point:

Accepted Answer

Correct answer: C. (c) L_1 :r= (-i+2j+k )+ (i+2j+k ) ⇒r= ( -1 )i+2 ( +1 )j+ ( +1 )k L_2 :r= (j+k )+ (2i+7j+3k ) ⇒r=2 i+ (1+7 )j+ (1+3 )k For point of intersection equating respective components ⇒ -1=2 2 ( +1 )=1+7 +1=1+3 We get ⇒ =3 and =1 ⇒a+b=3i+9j+4k L_3 :r=2i+8j+4k+ (3i+9j+4k ) For =2 ,r=8i+26j+12k

$Let a = i + 2 j + k and b = 2 i + 7 j + 3 k . Let L_{1} : r = (- i + 2 j + k) + λa, λ \in R and L_{2} : r (j + k) + μ b, μ \in R be two lines. If the line L_{3} passes through the point of intersection of L_{1} and L_{2}, and is parallel to a + b, then L_{3} passes through the point:$

Solution

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