Find the vector equation of the line passing through the point having position vector -2 i+j+k and parallel to vector 4 i-j+2 k

Find the vector equation of the line passing through the point ha…

$\int\limits^{1}_0\{\text{x}\}\text{dx},$ where {x} denotes the fractional part of x.

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Find the components along the coordinate axis of the position vector of the following point:R(-11, -9)

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Find the probability distribution of number of heads in two tosses of a coin.

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

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Evaluate $\int\frac{\sec^2\sqrt{\text{x}}}{\sqrt{\text{x}}}\text{ dx}$

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For the principal values, evaluate the following:
$\text{cosec}^{-1}\Big(2\tan\frac{11\pi}{6}\Big)$

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Write a 2×2 matrix which is both symmetric and skew-symmetric.

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Write the equation of the plane $\vec{\text{r}}=\vec{\text{a}}+\lambda\vec{\text{b}}+\mu\vec{\text{c}}$ in scalar product from.

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Find the vector projection of $P \vec{Q}$ on $A \vec{B}$ where P, Q, A, B are the points $(-2,1,3),(3,2,5)$ $(4,-3,5)$ and $(7,-5,-1)$ respectively.

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If $A =\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]$ and $A (\operatorname{adj} A )= KI$, then the value of ' $K$ ' is .....

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