Consider line L, given below. (a) Find point P that belongs to the line and direction...

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Consider line L, given below. (a) Find point P that belongs to the line and direction vector v of the line. Express v in component form. P = + V = x = 3 + t, y = 1 + t, z = 4 + 2t, tER (b) Find the distance from the origin to line L. Additional Materials eBook -/6.66 Points] DETAILS OSCALC1 12.5.254. Find the distance between point A(4, 5, 4) and the line of parametric equations x = -1 -t, y = -t, z = 2, tER. MY NOTES PRACTICE ANOTHER Consider lines 4₁ and L₂. L₁: x = 1 + t, y=t, z = 3 + t, te R, L₂: x-4=y-1=z-4 (a) Verify whether lines L₁ and L₂ are parallel. The lines ---Select--- parallel. (b) If the lines L₁ and L₂ are parallel, find the shortest distance between them. (If the lines are not parallel, enter NOT PARALLEL.) Consider point P and vector n. P(5, 4, 4), n = 4 + 5j - k (a) Find the scalar equation of the plane that passes through P and has normal vector n. (b) Find the general form of the equation of the plane that passes through P and has normal vector n. t Tutorial Additional Materials eBook 6.66 Points] DETAILS OSCALC1 12.5.271. Consider the equation of a plane. 3x + 4y + 6z - 12 = 0 (a) Find normal vector n to the plane. Express n using standard unit vectors. MY NOTES PRACTICE ANOTHER Consider line L, given below. (a) Find point P that belongs to the line and direction vector v of the line. Express v in component form. P = + V = x = 3 + t, y = 1 + t, z = 4 + 2t, tER (b) Find the distance from the origin to line L. Additional Materials eBook -/6.66 Points] DETAILS OSCALC1 12.5.254. Find the distance between point A(4, 5, 4) and the line of parametric equations x = -1 -t, y = -t, z = 2, tER. MY NOTES PRACTICE ANOTHER Consider lines 4₁ and L₂. L₁: x = 1 + t, y=t, z = 3 + t, te R, L₂: x-4=y-1=z-4 (a) Verify whether lines L₁ and L₂ are parallel. The lines ---Select--- parallel. (b) If the lines L₁ and L₂ are parallel, find the shortest distance between them. (If the lines are not parallel, enter NOT PARALLEL.) Consider point P and vector n. P(5, 4, 4), n = 4 + 5j - k (a) Find the scalar equation of the plane that passes through P and has normal vector n. (b) Find the general form of the equation of the plane that passes through P and has normal vector n. t Tutorial Additional Materials eBook 6.66 Points] DETAILS OSCALC1 12.5.271. Consider the equation of a plane. 3x + 4y + 6z - 12 = 0 (a) Find normal vector n to the plane. Express n using standard unit vectors. MY NOTES PRACTICE ANOTHER

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C onsider the line L given below X 3t y 1t z42t tR aFind point P that belongs to the line and direction vector v of the line Express v in component form P V The line L is given by the parametric equat... View the full answer