Two vectors  and  find the value of scalar x such that  is perpendicular to A :

Sure, let's solve this step by step. To find the value of the scalar $x$ such that the vector $B$ is perpendicular to the vector $A$, we need to use the concept of the dot product. Two vectors are perpendicular if and only if their dot product is zero.

Let's denote the vectors as: $\mathbf{A} = \begin{pmatrix} a_1 \\ a_2 \\ a_3 \end{pmatrix}$ $\mathbf{B} = \begin{pmatrix} b_1 \\ b_2 \\ b_3 \end{pmatrix}$

The dot product of $\mathbf{A}$ and $\mathbf{B}$ is given by: $\mathbf{A} \cdot \mathbf{B} = a_1 b_1 + a_2 b_2 + a_3 b_3$

For $\mathbf{B}$ to be perpendicular to $\mathbf{A}$, the dot product must be zero: $a_1 b_1 + a_2 b_2 + a_3 b_3 = 0$

Now, let's assume that the vector $\mathbf{B}$ is given in terms of the scalar $x$. For example: $\mathbf{B} = \begin{pmatrix} b_1 \\ b_2 \\ x \end{pmatrix}$

Substitute $\mathbf{B}$ into the dot product equation: $a_1 b_1 + a_2 b_2 + a_3 x = 0$

Now, solve for $x$: $x = -\frac{a_1 b_1 + a_2 b_2}{a_3}$

So, the value of the scalar $x$ that makes $\mathbf{B}$ perpendicular to $\mathbf{A}$ is: $x = -\frac{a_1 b_1 + a_2 b_2}{a_3}$

This is the step-by-step process to find the value of $x$. If you have specific values for the components of $\mathbf{A}$ and $\mathbf{B}$, you can substitute them into the equation to find the numerical value of $x$.