Question

A line passing through the point a with position vector a vector is equal to 2 i + 2 + 2 k is parallel to the vector

Answer 1

Explanation:

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Answer 2

Let A, B and C be the points with position vectors 2i - j + k, - i + 4j + k and i + 2k + 2k, respectively. We have to find the equation of a line passing through the point A and parallel to vector BC. Now, Vector BC = position vector of C − position vector of B = (i + 2j + 2k) - (-i + 4j + k) = 2i - 2j + k We know that the equation of a line passing through a point vector a and parallel to b is r = a + λb. Here, vector a = 2i - j + k So, the equation of the required line r = (2i - j + k) + λ(2i - 2j + k) (1) Reduction to Cartesian form by putting which is the Cartesian equivalent of Eq. (1).