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
Vector
2012-10-18 9:15 am
回答 (1)
2012-10-18 6:23 pm
✔ 最佳答案
Direction vector of the given line is -i - j, thus we can choose i - j as the direction vector of the required line.Hence the vector equation is:
(i + 2j) + p(i - j) where p is a real variable.
In parametric form, the given line is x = 1 - λ and y = 3 - λ
The required line is x = 1 + p and y = 2 - p
So we haev:
1 - λ = 1 + p and 3 - λ = 2 - p
Solving we have p = -1/2 and λ = 1/2
So the point of intersection is at (1/2. 5/2)
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