Q. 10
Find the equations of the line passing through the point (-1, 3, -2) and perpendicular to each of the lines 
and 
Answer :
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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Find the vector and Cartesian equations of the line through the point (1, 2, -4) and perpendicular to the two lines.
and 
Write the vector equations of the following lines and hence determine the distance between them:
