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a) Let u=(2,3,-1) and w=(3,-1,p). Given that u is perpendicular to w, find the value of p. b)Let v=(1,q,5). Given that modulus v = sqrt(42), find the possible values of q.

a) u is perpendicular to w , so u • w =0. This means that 2 3 + 3 (-1) + (-1)*p = 0, so 6-3-p=0, hence p=3. b) The magnitude of v = sqrt(1 2 +q 2 +5 2 ) = sqrt(42). Thus, 1+q 2 +25 = 42, q 2 =16, so q is eit...
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Answered by Cristiana R. • Maths tutor
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What is the difference between determinism and reductionism?

Reductionism is when complex behaviour is reduced to just one or two factors. For example, Behaviourism reduces complex learning down to just stimulus-response (e.g. classical conditioning), and the Biologic...
RW
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a) Given f(x) = ln(x), use the Mean Value Theorem to show that for 0 <a <b, (b-a)/b < ln(b/a) < (b-a)/a. b)Hence show that ln(1.2) lies between 1/m and 1/n, with m, n consecutive integers to be determined.

a) f(x)=ln(x), so f'(x)=1/x. By MVT, f'(c) = (f(b)-f(a))/(b-a) = (ln b - ln a)/(b-a) = ln(b/a)/(b-a), where c lies between a and b. Now, since 1/x is a decreasing function, and a &lt; c &lt; b, we get 1/b &l...
CR
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Explain Aquinas’ and Copleston’s Cosmological Argument

Finally, the third way of Aquinas’ five ways is the proof of God’s existence from contingency, which argues that God is a necessary being. Within this argument, Aquinas refers to contingent and necessary bei...
CF
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What are the key differences between direct realism and idealism?

Direct realism (or naïve realism) as a theory of perception claims that what we perceive are real objects and their properties, and that these objects exist without even minds to perceive them. This often se...
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Answered by Ola A. • Philosophy tutor
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