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
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)
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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