If a = i + j and b = i - k , then the point of intersection of the lines r a = b a and r b = a b is

Step-by-step solution

The given equations of the lines are r a = b a and r b = a b . From the first equation, we can write: r a - b a = 0 ( r - b ) a = 0 This implies that the vector r - b is parallel to a . Thus, r = b + a for some scalar . Similarly, from the second equation: r b - a b = 0 ( r - a ) b = 0 This implies that the vector r - a is parallel to b . Thus, r = a + b for some scalar . At the point of intersection, the position vector r must satisfy both conditions: b + a = a + b ( - 1) a + (1 - ) b = 0 Since a = i + j and b = i