Find symmetric equations for the line that passes through the point (5, -2, 7) and is parallel to the vector (-1, 3, -4). O* + 5 -1 y - 2 z + 7 3 -4 X - 5 y + 2 z - 7 -1 3 -4 O -(x + 5) = 3(y – 2) = -4(z + 7). 5 -(x - 5) = 3(y + 2) = -4(z - 7). Ox + 5 = Y + 2 3 z - 7 -4
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- Find the equation of the line that passes through the point (3,4,5) and is parallel to the vector product of the vectors (1,3, -5) and (-3,1,4).Find a vector equation of a line passing through the point (-1, -2, 4) and perpendicular to botha = [0, − 1, 7] and b = [ ,4,2 − 3] .Write down the vector equation of the line that passes through the points (x,y,z) = (2,3,7) and (x,y,z)= (4,1,2)
- Find symmetric equations for the line through the point (1, -2, -4) which is orthogonal to the plane 2x−y+3z=182x−y+3z=18.Find two vectors v1 and v2 whose sum is <0,−4>, where v1 is parallel to <−1,−5> while v2 is perpendicular to <−1,−5>. v1 = ? and v2 = ?.5. Find the equation of the plane that is parallel to the vectors 3,0,1 and 0,1,2, passing through the point (1,0,−4).
- find a vector that is perpendicular to the line 3x-4y=6If P1 is (1,3,-1) and P2 is (-3,2,4), find the vector equation of the line P1P2. Determine the intersection of the line with the x = 0 plane, y=0 plane and z=0 planeFind equations of the line through the point (1, −1, 1) perpendicular to the line 3x = 2y = z and parallel to the plane x + y − z = 0.