If b is a unit vector such that ( a + b ). ( a - b )=8, find | a |.

Given that b is a unit vector. | b |=1 And ( a + b ). ( a - b )=8 (Given) | a |^2- | b |^2=8 | a |^2-1^2=8 | a |^2=9 | a |=3

If b is a unit vector such that ( a + b ). ( a - b )=8, find

If $\text{A}=\begin{bmatrix}4&3\\1&2 \end{bmatrix}$ and $\text{B}=\begin{bmatrix}-4\\3\end{bmatrix},$ write AB.

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If P (A) = $\frac{3}{5}$ and P (B) = $\frac{1}{5}$ find P ($A \cap B$) if A and B are independent events.

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Evaluate the following determinant: $\begin{vmatrix}67&19&21\\39&13&14\\81&24&26 \end{vmatrix}$

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If $\text{f(x)}=\begin{cases}\frac{1-\cos\text{x}}{\text{x}^2},&\text{x}\neq0\\\text{k},&\text{x}=0\end{cases}$ is continuous at x = 0, find k.

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Evaluate the following integrals:
$\int\limits^2_0\sqrt{4-\text{x}^2}\text{ dx}$

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Write the projection of $\vec{\text{r}}=3\hat{\text{i}}-4\hat{\text{j}}+12\hat{\text{k}}$ on the coordinate axes.

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Find the value of k so that the lines x = -y = kz and x - 2 = 2y + 1 = -z + 1 are perpendicular to each other.

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A discrete random variable $X$ has the probability distribution given below:

$X:$	$0.5$	$1$	$1.5$	$2$
$P(X):$	$k$	$k^2$	$2k^2$	$k$

Find the value of $k.$

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Find the values:
$\sin^{-1}\bigg(\sin\frac{2\pi}{3}\bigg)$

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If $\begin{bmatrix}2\text{x}+1&5\text{x}\\0&\text{y}^2+1\end{bmatrix}=\begin{bmatrix}\text{x}+3&10\\0&26\end{bmatrix},$ find the value of (x + y).

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