The vector equation of the line passing through points $A(3,4,-7)$ and $B(1,-1,6)$ is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\vec x=(3-2λ)\hat i+ (4 − 5λ)\hat j + (-7 +13λ)\hat k$
Points are $A(3,4,-7)$ and $B(1,-1,6)$.
Direction vector $\vec{AB}=(1-3,\,-1-4,\,6-(-7))=(-2,-5,13)$.
Vector equation of the line through $A$ in direction $\vec{AB}$:
$\vec x=\vec a+\lambda\vec{AB}$
$\vec x=(3,4,-7)+\lambda(-2,-5,13)$
$\vec x=(3-2\lambda)\hat i+(4-5\lambda)\hat j+(-7+13\lambda)\hat k$
Final answer: $\vec x=(3-2\lambda)\hat i+(4-5\lambda)\hat j+(-7+13\lambda)\hat k$