Find the domain of the ctor function. (Enter your answer using interval notation.) r(t) = (In(t + 2), t √64=+2+ 24)
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- Q2. ()- Work out a - 2b as a column vector.Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) = √ 25 ✓ 25 t2 i + t²j - 4tk -Find an equation of the line, 1(t), containing the points (1, 3, 1), (2, −3, 2), and (5, 7, 2). (Write your answer in the vector form (*, *, *). Enter the symbol for the empty set, Ø, if the points do not lie on the same line.) l(t) = =
- Find an equation of the line, 1(t), containing the points (1, 3, 1), (2, −3, 2), and (5, 7, 2). (Write your answer in the vector form (*, *, *). Enter the symbol for the empty set, Ø, if the points do not lie on the same line.) 1(t) =Let a, b, and x denote vectors in Rn. (a) Simplify 3a + (5b -2a) + 2(b -a). (b) If 5x - a = 2(a + 2x), solve for x in terms of a.Q2. What will be the effect of multiplying the vector by a positive and a negative scalar. Explain in details the effect of each .case
- 2. Determine whether the expression is defined or undefined. If it is defined, then determine whether it is a vector or a scalar. If it is undefined, explain why. a xỉ a. b. ||à × ī|| c. (ā× b) + (è ×ā) d. (āxb).c e. (ā·b) + č f. (a.b) + (c. d) + 3 g. a. (b.c)Use the given vectors to answer the following questions. a = (3, 2, 4), = (-3, 3, 0), c = (0, 0, –2) b (a) Find a x (b × c). * (b x c) = || (b) Find (a x b) x c. (a x b) x c =Vector Calculus. Please fill in all necessary solutions. Thanks.