Thread: Parallel vectors? and vector sum questions

I have two vectors: t i - j + k and ti + t j -- 2k t is some coefficient. I know that to make these vectors perpendicular t = 2 but I am asked whether there is a value of t to make these vectors parallel. I could not find any scaler value to make this true. Am I missing something or am I correct?


I have been asked to write vector a which is 3i + 2j - 6k as the sum of two vectors, oone parallel, and one perpendicular to vector d which = 2i - 4j + k

I am stumped. I realize that for the first vector that is parallel to vector d it will just be a scaler times vector d and I know that the second vector's dot product with a must equal 0 but........ THe answer is given as - 8/21 d + 79/21 i + 10/21 j - 118/21 k

Thanks to all of you helpful folks. YOu have helped me complete two courses of calculus and I am now on my last required one!!!!

Hi

Note that for the first question not only t=2 but also t=-1 give perpendicular vectors. There is no possibility to get parallel vectors.

For the second question see the sketch where u = 3i + 2j - 6k and d = 2i - 4j + k



You can see that the dot product of u and d is :
u.d = (td).d = t (d.d)

Therefore t = d.d / u.d