The parametric equations of the line passing | vedclass

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Question

(A) The line passes through points $A(3, 4, -7)$ and $B(1, -1, 6)$.First,find the direction vector $\vec{v} = B - A = (1 - 3, -1 - 4, 6 - (-7)) = (-2,

Vedclass · Accepted Answer

$x = 3 - 2\lambda, \quad y = 4 - 5\lambda, \quad z = -7 + 13\lambda$

Vedclass · Answer

(A) The line passes through points $A(3, 4, -7)$ and $B(1, -1, 6)$.First,find the direction vector $\vec{v} = B - A = (1 - 3, -1 - 4, 6 - (-7)) = (-2, -5, 13)$.The parametric equations of a line passing through $(x_1, y_1, z_1)$ with direction vector $(a, b, c)$ are given by $x = x_1 + a\lambda, y = y_1 + b\lambda, z = z_1 + c\lambda$.Using point $A(3, 4, -7)$ and direction vector $(-2, -5, 13)$,we get:$x = 3 - 2\lambda$$y = 4 - 5\lambda$$z = -7 + 13\lambda$Thus,the correct option is $A$.

The parametric equations of the line passing through $A(3, 4, -7)$ and $B(1, -1, 6)$ are:

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