Find a unit vector along perpendicular to vectors (a+b) and (a-b) where a=2 i+j-2 k and b=i-2 j+2 k.

Find a unit vector along perpendicular to vectors (a+b) and (a-b)…

Find matrix $\text{A},\text{if}\begin{bmatrix}1&2&-1\\0&4&9\end{bmatrix}+\text{A}=\begin{bmatrix}9&-1&4\\-2&1&3\end{bmatrix}$

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Write a value of $\int\frac{(\log\text{x})^{\text{n}}}{\text{x}}\text{ dx}$

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Solve the following system of homogeneous linear equations:

2x + 3y + 4z = 0,

x + y + z = 0,

2x - y + 3z = 0

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Show that the following planes are at right angles. $x - 2y + 4z = 10$ and $18x + 17y + 4z = 49$

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If $\text{y}=\sin\text{x}$ and x changes from $\frac{\pi}{2}$ to $\frac{22}{14}$, what is the approximate change in y?

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Find fog and gof if: $f(x) = x^2, g(x) = \cos x$

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Evaluate the following integrals:
$\int_{0}^\limits{1}\frac{\sqrt{\tan^{-1}\text{x}}}{1+\text{x}^2}\text{ dx}$

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Evaluate the following integrals:
$\int5^{\text{x}+\tan^{-1}\text{x}}.\Big(\frac{\text{x}^2+2}{\text{x}^2+1}\Big)\text{dx}$

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Show that the line through points $(1, -1, 2)$ and $(3, 4, -2)$ is perpendicular to the line throught the points $(0, 3, 2)$ and $(3, 5, 6).$

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Find the mean and standard deviation of the following probability distributions:

$x_i$	$1$	$2$	$3$	$4$
$p_i$	$0.4$	$0.1$	$0.2$	$0.3$

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