Two lines r = a 1+λ b 1 and r = a 2+μ b 2 are said to be coplanar, if

Question

Two lines r = a 1+λ b 1 and r = a 2+μ b 2 are said to be coplanar, if (A) (a2-a1) ⋅(b1 × b2)=0 (B) | x 1 y 1 z 1 a 1 b 1 c 1 a 2 b 2 c 2|=0 where ( x 1, y 1, z 1) are the coordinates of a point on any of the line and a 1, b 1, c 1 and a 2, b 2, c 2 are the direction ratio of b 1 and b 2 (C) Both (a) and (b) (D) None of the above

Tardigrade Admin · Accepted Answer

Correct answer is (a) (a2-a1) ⋅(b1 × b2)=0

Q. Two lines $r = a_{1} + λ b_{1}$ and $r = a_{2} + μ b_{2}$ are said to be coplanar, if

$(a_{2} - a_{1}) \cdot (b_{1} \times b_{2}) = 0$

$∣ ∣ x_{1} a_{1} a_{2} y_{1} b_{1} b_{2} z_{1} c_{1} c_{2} ∣ ∣ = 0$ where $(x_{1}, y_{1}, z_{1})$ are the coordinates of a point on any of the line and $a_{1}, b_{1}, c_{1}$ and $a_{2}, b_{2}, c_{2}$ are the direction ratio of $b_{1}$ and $b_{2}$

Both (a) and (b)

None of the above

Correct answer is (a) $(a_{2} - a_{1}) \cdot (b_{1} \times b_{2}) = 0$

Q. Two lines r=a1​+λb1​ and r=a2​+μb2​ are said to be coplanar, if

(a2​−a1​)⋅(b1​×b2​)=0

∣∣​x1​a1​a2​​y1​b1​b2​​z1​c1​c2​​∣∣​=0 where (x1​,y1​,z1​) are the coordinates of a point on any of the line and a1​,b1​,c1​ and a2​,b2​,c2​ are the direction ratio of b1​ and b2​