Question

A vector equation for a given straight line is r = (i + 3j) + lambda (-i - j)

Construct a vector equation for the line that does go through the point (1,2), and is perpendicular to r.

and

Determine the point of intersection of the two lines

Answers

you know that i-j is perpendicular to -i-j since (-1)(1) + (-1)(-1) = -1+1 = 0

so, i+2j + alpha(i - j) will do the trick

1-lambda = 1 + alpha
3-lambda = 2 - alpha

intersect where lambda = 1/2 alpha = -1/2, at the point (1/2,5/2)

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