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Direction ratios of a vector parallel to line (x–1)/2 = – y = (2z+1)/6 are :
The lines (1–x)/2 = (y–1)/3 = z/1 and (2x–3)/2p = y/(–1) = (z–4)/7 are perpendicular to each other for p equal to:
Find the distance between the line x/2 = (2y – 6)/4 = (1 – z)/(–1) and another line parallel to it passing through the point (4, 0, –5).
If the lines (x – 1)/(–3) = (y – 2)/(2k) = (z – 3)/2 and (x – 1)/(3k) = (y – 1)/1 = (z – 6)/(–7) are perpendicular to each other, find the value of k and hence write the vector equation of a line perpendicular to these two lines and passing through the point (3, –4, 7).
The Cartesian equation of the line passing through the point (1, −3, 2) and parallel to the line r⃗ = (2 + λ)î + λĵ + (2λ − 1)k̂ is :
Find the vector equation of the line passing through the point (2, 3, −5) and making equal angles with the co-ordinate axes.
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