The dimensions of the vectors are mismatched.  

Since vector $\displaystyle \vec{a}$ does not have the same dimensions as $\displaystyle \vec{b}$, the answer for $\displaystyle 2\vec{a}-6\vec{b}$ cannot be solved.

To find the vector form of $\displaystyle 2i-10k$, we must map the coefficients of $\displaystyle i$, $\displaystyle j$, and $\displaystyle k$ to their corresponding $\displaystyle x$, $\displaystyle y$, and $\displaystyle z$ coordinates. Thus, $\displaystyle 2i-10k$ becomes $\displaystyle \left \langle 2,0,-10\right \rangle$.

In order to express $\displaystyle -2i+7j-10k$ in vector form, we must use the coefficients of $\displaystyle i, j,$and $\displaystyle k$ to represent the $\displaystyle x$-, $\displaystyle y$-, and $\displaystyle z$-coordinates of the vector.

Therefore, its vector form is 

$\displaystyle \left \langle -2,7,-10\right \rangle$.

In order to express $\displaystyle i+5k$ in vector form, we must use the coefficients of $\displaystyle i, j,$and $\displaystyle k$ to represent the $\displaystyle x$-, $\displaystyle y$-, and $\displaystyle z$-coordinates of the vector.

Therefore, its vector form is 

$\displaystyle \left \langle 1,0,5\right \rangle$.

In order to express $\displaystyle 4i-9j$ in vector form, we must use the coefficients of $\displaystyle i, j,$and $\displaystyle k$ to represent the $\displaystyle x$-, $\displaystyle y$-, and $\displaystyle z$-coordinates of the vector.

Therefore, its vector form is 

$\displaystyle \left \langle 4,-9,0\right \rangle$.

In order to express $\displaystyle -j+7k$ in vector form, we will need to map its $\displaystyle i$, $\displaystyle j$, and $\displaystyle k$ coefficients to its $\displaystyle x$-, $\displaystyle y$-, and $\displaystyle z$-coordinates.

Thus, its vector form is 

$\displaystyle \left \langle 0,-1,7\right \rangle$. 

In order to express $\displaystyle 5i+9j-2k$ in vector form, we will need to map its $\displaystyle i$, $\displaystyle j$, and $\displaystyle k$ coefficients to its $\displaystyle x$-, $\displaystyle y$-, and $\displaystyle z$-coordinates.

Thus, its vector form is 

$\displaystyle \left \langle 5,9,-2\right \rangle$. 

In order to express $\displaystyle -2i+3j$ in vector form, we will need to map its $\displaystyle i$, $\displaystyle j$, and $\displaystyle k$ coefficients to its $\displaystyle x$-, $\displaystyle y$-, and $\displaystyle z$-coordinates.

Thus, its vector form is 

$\displaystyle \left \langle -2,3,0\right \rangle$. 

To find the vector form of $\displaystyle 4i+4j-2k$, we must map the coefficients of $\displaystyle i$, $\displaystyle j$, and $\displaystyle k$ to their corresponding $\displaystyle x$, $\displaystyle y$, and $\displaystyle z$ coordinates.

Thus, $\displaystyle 4i+4j-2k$ becomes $\displaystyle \left \langle 4,4,-2\right \rangle$.

To find the vector form of $\displaystyle -9j+k$, we must map the coefficients of $\displaystyle i$, $\displaystyle j$, and $\displaystyle k$ to their corresponding $\displaystyle x$, $\displaystyle y$, and $\displaystyle z$ coordinates.

Thus, $\displaystyle -9j+k$ becomes $\displaystyle \left \langle 0,-9,1\right \rangle$.