If a and b are two vectors such that ( a + b ). ( a - b ).=0, find the relation betwen the magnitudes of a and b .

Given that ( a + b ). ( a - b )=0 | a |^2- | b |^2=0 | a |^2= | b |^2 | a |= | b |

If a and b are two vectors such that ( a + b ). ( a - b ).=0, fin…

If $\begin{bmatrix}2\text{x+y}&3\text{y}\\0&4 \end{bmatrix}=\begin{bmatrix}6&0\\6&4\end{bmatrix}$, then find x.

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In each of the following examples verify that the given expression is a solution of the corresponding differential equation.

$y=x^{ m } ; x^2 \frac{d^2 y}{d x^2}-m x \frac{d y}{d x}+m y=0$

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Evalute the following integrals:
$\int\frac{1}{\sqrt{\text{x}}(\sqrt{\text{x}}+1)}\text{dx}$

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Find the general solution of : $\sec \theta+\sqrt{2}=0$

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Evaluate:
$\int \frac{2 x-7}{\sqrt{4 x-1}} \cdot d x$

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Find the of the polar co-ordinates point whose Cartesian co-ordinates are. :

$(\sqrt{2}, \sqrt{2})$

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A matrix of order $3 \times 3$ has determinant $2$. What is the value of $|A(3I)|$, where I is the identity matrix of order $3 \times 3$.

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If the normal to the plane has direction ratios 2, −1, 2 and it’s perpendicular distance from origin is 6, find its equation

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Find the of the polar co-ordinates point whose Cartesian co-ordinates are. :

$(1,-\sqrt{3})$

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Integrate the following functions w.r.t. x:

$\left[\frac{x}{(x+1)^2}\right] e^x$

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