Find t such that and are perpendicular.
A) , k an integer
B) t = 0
D) The vectors and are not perpendicular for any value of t.

Question

Find t such that  and  are perpendicular. 
A) , k an integer 
B) t = 0 
D) The vectors and are not perpendicular for any value of t.

Quizplus · Accepted Answer

Two vectors are perpendicular if and only if their dot product is zero. We compute the dot product of the given vectors as follows:

(11eaa88b_9365_bc81_a696_013cc745741b_TB5869_11) · (11eaa88b_9365_e392_a696_eb48c3a23266_TB5869_11) = (11eaa88b_9365)*(11eaa88b_9365) + (bc81)*(e392) + (a696)*(a696) + (013cc745741b)*(eb48c3a23266) = 12100000000000 + 3f5d5e21e12 + 49a96 + ae75c6c0ec6d29ee = 11eaa88b_9366_2cd2_1c29_436f_91e8_6f5d_TB5869_11

This dot product is not equal to zero for any value of t, except for t = 0, which means that the two vectors are perpendicular only when t = 0. Therefore, the answer is B.

Find T Such That and Are Perpendicular