Q2c) determine the value(s) of k so that the vectors u=(2k,-1,7)and v=(k,k,-3) are perpendicular.?

Answer 1

If the vectors are perpendicular then the dot product of the vectors will equal zero.

u • v = <2k, -1, 7> • = 2k² - k - 21 = 0

Now we have a quadratic equation in k to solve.

2k² - k - 21 = 0
(2k - 7)(k + 3) = 0
k = 7/2, -3