Find parametric equations for the lines in The line through the origin parallel to the vector 2j + k

Find parametric equations for the lines in The line through the origin parallel to the vector 2j + k

Question
Find parametric equations for the lines in The line through the origin parallel to the vector \(2j + k\)

Answers (1)

2021-02-13
Step 1 Given The vector equation is \(0i + 2j + k\) The line passing through origin , origin is ( 0 ,0 ,0) The parametric equations for the line passing through the point \(p0 = ( x_0 ,y_0 ,z_0 )\) and parallel to the vector is \(v =(ai + bj + ck)\)
\(x = x_0 + at , y = y_0 + bt , z = z_0 + ct\) Step 2 To find parametric equations for the lines Here \(a = 0 , b = 2 , c = 1 , x_0 = 0 ,y_0 = 0 and z_0 = 0\) Now plug this values in parametric equation \(x = 0 + 0t , y = 0 + 2t , z = 0 + 1t\)
\(x = 0 , y = 2t , z = t\) Therefore parametric equations for the line is \(x = 0 , y = 2t and z = t\) .
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