question archive Question 1: Let vectors: A? =(2,1,−4), B? =(−3,0,1), and C? =(−1,−1,2)

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Question 1:

Let vectors: *A*? =(2,1,−4), *B*? =(−3,0,1), and *C*? =(−1,−1,2).

Calculate the following:

(A) What is the value of *A*? ⋅ *B*? ?

(B) What is the angle *θ*AB between *A*? and *B*? ?

(C) What is the value of 2*B*? ⋅ 3*C*? ?

(D) What is the value of 2(*B*? ⋅ 3*C*?) ?

Which of the following can be computed? (Choose only 1 of the following)

A? ⋅B? ⋅C? |

A? ⋅(B? ⋅C? ) |

A? ⋅(B? +C? ) |

3⋅A? |

FOR PARTS F THROUGH H:

*V*? 1 and *V*? 2 are different vectors with lengths *V*1 and *V*2 respectively. Find the following:

(F) Express Answer in terms of *V*? 1, *V*? 1⋅*V*? 1 =

(G) If *V*? 1 and *V*? 2 are perpendicular, *V*? 1⋅*V*? 2 =

(H) Express your answer in terms of *V*1 and *V*2. If *V*? 1 and *V*? 2 are parallel, *V*? 1⋅*V*? 2 =

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