Q. 10

# Find the equation

Given: line passes through (-1, 3, -2) and is perpendicular to each of the lines and

To find: equation of line in Vector and Cartesian form

Formula Used: Equation of a line is

Vector form:

Cartesian form:

where is a point on the line and is a vector parallel to the line.

If 2 lines of direction ratios a1:a2:a3 and b1:b2:b3 are perpendicular, then a1b1+a2b2+a3b3 = 0

Explanation:

Here,

Let the direction ratios of the line be b1:b2:b3

Direction ratios of the other two lines are 1 : 2 : 3 and -3 : 2 : 5

Since the other two line are perpendicular to the given line, we have

b1 + 2b2 + 3b3 = 0

-3b1 + 2b2 + 5b3 = 0

Solving,

Therefore,

Vector form of the line is:

Cartesian form of the line is:

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