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Given the vectors u = 3i - 2j + k, v = i + 2j - 4k, w = -2i + 4j - 5k use vector methods to answer the following:
(a) Prove u, v and w can form the sides of a triangle;
(b) Find the vector projection of u on v;
(c) Find the angle between u and v (to nearest degree);
(d) Find a unit vector normal (perpendicular) to the plane of the triangle in (a).
Rate - when we know how many objects are in a set, and need to find out the total number in several copies of that set. (e.g., if a child uses 4 copybooks in a year, how many co
If 7 cosec?-3cot? = 7, prove that 7cot? - 3cosec? = 3. Ans: 7 Cosec?-2Cot?=7 P.T 7Cot? - 3 Cosec?=3 7 Cosec?-3Cot?=7 ⇒7Cosec?-7=3Cot? ⇒7(Cosec?-1)=3Cot? ⇒7(C
Volumes for Solid of Revolution Before deriving the formula for it we must probably first describe just what a solid of revolution is. To find a solid of revolution we start o
The manager of a specialty store marks up imported products 110%. If a vase imported from Italy costs him $35, what price tag will he put on the item? To ?nd out the price he s
PROOF OF VARIOUS DERIVATIVE FACTS/FORMULAS/PROPERTIES Under this section we are going to prove several of the different derivative facts, formulas or/and properties which we en
(1) Prove that Zorn's lemma is equivalent to axiom of choice. (2) Use Zorn's Lemma to prove the existence of E.
Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.
Write an algebraic expression for “Julie runs three miles less than twice the number of miles,
How many relations are possible from a set A of 'm' elements to another set B of 'n' elements? Ans: A relation R from a set A to other set B is specified as any subset of A
Evaluate following sin 2 ?/3 and sin (-2 ?/3) Solution: The first evaluation in this part uses the angle 2 ?/3. It is not on our unit circle above, though notice that 2 ?/
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