=µ ‌N(12µ−8,5µ−2,9µ−11) ‌MN=(4λ−12µ+13,λ−5µ+6,3λ−9µ+16) .......(1) Now
→
b
1×
→
b
2=|
^
i
^
j
^
k
4
1
3
12
5
9
|=−6
^
i
+8
^
k
.............(2) Equation (1) and (2) ∴‌
4λ−12µ+13
−6
=‌
λ−5µ+6
0
=‌
3λ−9µ+16
8
I and II λ−5µ+6=0 ..........(3) I and III λ−3µ+4=0 ............(4) Solve (3) and (4) we get ‌λ=−1,µ=1 ‌∴M(1,3,2) ‌N(4,3,−2) ‌∴