MTH303
Question: The Stoke’s theorem uses which of the following operation?
Answer: Curl
Question: If \\(A=3i-j+2k\\) and \\(B=2i+3j-k\\), find the cross product \\(A \\times B\\)
Answer: \\(-5i+7j+11k\\)
Question: Given that \\(\\overline{a}=2i + j -3k\\) and \\(\\overline{b}=i +x j +4k\\) are perpendicular, find the value of \\(x\\)
Answer: 10
Question: Find the modulus of the vector \\(\\overline{r}=cos (t^2)I + sin (t^2)j\\)
Answer: 1
Question: Find the unit vector in the direction of the vector \\(\\overline{r}=8i – 3j +2k\\)
Answer: \\( \\frac{8i – 3j+2k}{\\sqrt{77}}\\)
Question: Determine the \\( curl F\\) at point (2, 0, 3) given that \\(F=xzi+(2x^2-y)j-yz^2k.
Answer: \\(-9i+8k\\)
Question: Given that \\(\\overline{r}= t^2i -tj+(2t+1)k\\) and \\(\\overline{s}= (2t-3)i +j -tk\\), find \\(\\frac{d}{dt}(\\overline{r}+\\overline{s})\\) at \\(t=1\\)
Answer: 4i – j+k
Question: Given that \\(\\psi = 2x^2y-xz^3\\), find \\(\\nabla^2 \\psi\\)
Answer: \\(4y-6xz\\)
Question: Find the angle between the two vectors \\(\\overline{p}=3i +j -k\\) and \\(\\overline{q}= 3i – j +2k\\)
Answer: \\(61.08^o\\)
Question: Given that \\(\\overline{F}= (3t^2+4t)I +(2t-5)+4t^3k\\), then evaluate \\(\\int_0^3 \\overline{F}dt\\)
Answer: 42i-2j+80k
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