MTH282
At any point of the path x=3cosâ?jt,y=3sinâ? jt,z=4t, find the Tangent vector. \n
Answer: -3 sinâ?jt i+3 cosâ?jt j+4k
Suppose that \( \alpha=2i-3j+k\) and \ (\Deta=7i-5j+k\), find a unit vector perpendicular to \(\alpha\) and \(\deta) respectively.
Answer: \\(\\frac{2i+5j+11 k }{5\\sqrt(6)}\\\
A stone moves along the path \( x=tA3+1 ,y=tA3\), \( z=2t+5\), where t denote time. What is the component of \((dp)/dt\) ?
Answer: 3i+2j+2k
If \(G â/—= ä€-5t䀗A2 i + tj – tA3 k\) and \( F â/— = sin ti – cost j\), what is \( d/dt (G. F â/—)\) ?
Answer: \\(100t^3+2t+ 6tA^\\)
is an example of scalar quantity.
Answer: mass
Vectors with same direction, same a sense (same arrow) but different magnitude are called
Answer: like vectors
If \(Gâ/—= ä€-5t䀗A2 i + tj – tA3 k\) and \ (F ä/— = sin ti – cost j\), what is \( d/dt (G Wtimes F â/—)\) ?
Answer: \\((tA3 sin t- 3tA2 cost)i-(tA3 cosä?j(t- 3tA2 sinâ?jt) j+(5tA2 sinâ?jâ€-t-sinâ?jâ€-t- 111 cost) k\\)䀗 䀗 䀗
The principal value of the argument of \ ((1+iâ’s3)(1-i)\) is
Answer: \\(\\fra{\\pi}{12}\\)
At any point of the path x=3cosâ?jt,y=3sinâ? jt,z=4t, what is the Normal vector?
Answer: \\(1/25 (-3 cosâ?jt i-3 sinâ?ît j )\\)
Solve for z if \((z-2)A2+16=0\).
Answer: \\(2\\pm 4i)
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