Question 1 5 pts Suppose u and U are nonzero vectors in three dimensions Indicat
ID: 2884160 • Letter: Q
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Question 1 5 pts Suppose u and U are nonzero vectors in three dimensions Indicate whether the following statements MUST be True, False, or that not enough information has been provided to determine this Note: The subscripts in the expressions below are vectors due to typesetting limitations in Canvas. 1. lf and i are not parallel, scali, ii liik Select 2. If it and it are not paralle scala, il Iscalu i Select 3. If u and a are orthogonal projuu [Select] 4. scala, il 0 Select 1 5. lf u is not parallel to v then (ux T) x u Select 6. If u is not parallel to v then projuv is parallel to i Select l proj u is perpendicular to i SelectExplanation / Answer
1. Scalar projection of U in the direction of V is Ucos( theta ) where theta is the angle between the two vectors. Since U * cos ( theta ) will always be <= |u| ( as cos (theta) will be less than or equal to 1). Hence false
2. |scalvU| = U.V/|V|; similarly |scalu V| = U.V/|U|
Which among these is greater depends on the |U| and |V| which is not given. Hence the given statement is false.
3. If the vectors are orthogonal, then the angle between them is 90 => cos 90 = 0 => U.V=0
Since projvU = (U.V/ |V|2 )V => projvU =0. True
4. ScaluU = U.U/|U| => angle between U and U is 0. Thus it is nott 0. False
5. If U is not parallel to V, then ( U X V) X U => U X V is a vector perpendicular to both U and V. This resultant when cross product with U then the product is not zero since the angle between the resultant of U X V and U is 90 and sin 90 =1 . False
6. ProjuV is projection of V in the direction of U. Hence this is parallel to U. True
7. U - projvU is not necessarily perpendicular to V. False
8. U - projvU is not necessarily perpendicular to V. Hence its dot product with V is not zero.
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