Dot products As a rule, - will only be used to denote the dot product of vectors, and not vector scaling or multiplication of real numbers. Vector scaling will be denoted A5, where A (the Greek letter 'lambda') denote-1 a real number; for instance, 26 denote-1 scaling by 2, whereas 2 '1'! is meaningless. 1. Which of the following expressions is meaningful, and which is meaningless? All of if, 111', 21' are vectors in R3. a)('5' ('5' U" E: C -w+u. ) )17' d) lllli'i' 8) [17' MN 13)- 1?! (13 + 11'}. 2. Compute 1? - all for the following pairs of vectors. a) (2, 3) - (2, 3). l (2' 3) ' (3' 2)- ) (2. 3) - {~3,2). d) (2. 3) - (Ht)- 3. Determine whether the angle between the following vectors is acute, perpendicular. or obtuse. Do not attempt to compute the actual value of the angle. (In particular, do not use a calculator.) a) The vectors (2, 3) and (3, 2). b) The vectors (1, 4, 2) and (3,1,1). c) The vectors (1,1,1,1) and (1, 2,3, 4). d) The vectors (2, 1) and (2, 4). 4. Suppose you know that 13' and 15 meet at an angle of 17/3 radians. Further, suppose you know that \"ll - 3 and ||1I3|| .... 4. With no further information, compute the dot product 13' ' 1.3. 5. Find the value of m so that (1, 1:, 3) and (2, 1, 1) are perpendicular. 6. Find all vectors (1:,y, 2) which is perpendicular to both (1, U, 1) and (U, 1, 1). (There are many.)