Q15
(i) Show that the line r^→ =i^{^}+j^{^}+λ(2i^{^} +j^{^} +4k^{^}) lies in the plane r(i^{^} +2j^{^}-k^{^}) =3.

(ii) If the line

x-2 / 3

=

y-1 / -5

=

z+2 / 2

lies in the plane x + 3y — αz + β = 0, then find the values of α and β.

(iii) Show that the line r^→ =(2i^{^}- 2j^{^}+3k^{^})+λ(i^{^}-j^{^}+4k^{^}) is parallel to the plane r^→(i^{^}+5j^{^}+k^{^}) =7.

Solution

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