Determine the value(s) of k such that (2k, 3, k+1) x (k-1, k, 1) = (1, -2, 2)?

1 Answer
Apr 28, 2017

#k=1#

Explanation:

Cross product of #(x_1,y_1,z_1)# and #(x_2,y_2,z_2)# is given by

#(y_1z_2-y_2z_1,z_1x_2-z_2x_1,x_1y_2-y_1x_2)#

Hence cross product of #(2k,3,k+1)# and #(k-1,k,1)# is

#((3xx1-k(k+1)),((k+1)(k-1)-1xx2k),(2kxxk-3(k-1))#

or #(3-k^2-k,k^2-1-2k,2k^2-3k+3)#

As it is #(1.-2.2)#, we have

#3-k^2-k=1# i.e. #k^2+k-2=0# i.e. #k=-2# or #k=1# and

#k^2-2k-1=-2# i.e. #k^2-2k+1=0# i.e. #k=1# and

#2k^2-3k+3=2# i.e. #2k^2-3k+1=0# i.e. #k=1/2# or #k=1#

As value of #k# should hold for all components of vector.

we have #k=1#