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choose y in order that the Vectors a=7i+yj+k, b=3i+2j+k, c=5i+3j+k are linearly dependent.

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Prove that [a+b,b+c,c+a]=2[a b c]

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Gradient in orthogonal curvilinear coordinate system.

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Solve (D²+2)y = x²e³^x.

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Solution:-

L-Hopital rule.

L-Hopital rule states that when the limit of f(x)/g(x) is indeterminate(0/0 form) in that conditions the value of limit can be obtained by evaluating  the derivatives of  f(x) and g(x) i.e[f'(x)/g'(x)].

Isoelectronic principle.

“Isoelectronic molecular species (I.e species having same number of atoms and same number of total valence electrons) have similar molecular orbitals and similar molecular structure.”

Bond order.

It is defined as the number of covalent bonds in a molecule.Bond order is equal to one half of the difference between the number of electrons in the bonding (Nb) and anti-bonding (Na) molecular orbitals.   I.e Bond order =1/2 (Nb-Na)