Question

1. Letū,7, andū be arbitrary non-zero vectors in 3-dimensional space. Determine which of the following best describes each product. Very briefly explain your answer. (i) a scalar, (ii) a vector, (iii) 0. (iv) 7 (v) undefined a) ūū b) (V xw.v c) (ū.w). (ü.w) d) (ü x w) x (2ú xw) e) ( iv) f) (u xv) xw g) (ü xv).

Answer 1

dot product of conta a because scalar doot product gives a scalar quantity Ha (2x). O V xw will give a vector perpendicular to it and is, and that the dot froduct with i will give formula to) - RO).(Q.) = undefined The dot braduct of two vectors gives us a scalar quantity and two scabar quantities cannot be det producted id - là x W) x (2 ü x ) = 3 u Xw will me vector as te will be parallel to each others so cross product of Lue parallel meters is gens 22x and give

a and 10- (Q W) x y z undefined Q. i will give us salar quantity cross product between a yector and a scalar quantity is undefined 10 - (u Xu) xw = undefined Cross product of scalar wantity is undefined (u X o o owo a vector ♡ Xu will give a vector and dot product of that vector to a will also give o us a a vectos