Write the vector $\mathbf{u}=\langle 6,-9\rangle$ in $\mathbf{i}, \mathbf{j}$ form. Written in $\mathbf{i}, \mathbf{j}$ form, the vector $\mathbf{u}=\langle 6,-9\rangle=$

Step 1 ：Write the vector \(\mathbf{u}=\langle 6,-9\rangle\) in \(\mathbf{i}, \mathbf{j}\) form.

Step 2 ：Written in \(\mathbf{i}, \mathbf{j}\) form, the vector \(\mathbf{u}=\langle 6,-9\rangle\)

Step 3 ：The vector \(\mathbf{u}=\langle 6,-9\rangle\) can be written in \(\mathbf{i}, \mathbf{j}\) form by multiplying the first component of the vector by \(\mathbf{i}\) and the second component by \(\mathbf{j}\). This is because \(\mathbf{i}\) and \(\mathbf{j}\) are the unit vectors in the x and y directions respectively.

Step 4 ：Final Answer: The vector \(\mathbf{u}=\langle 6,-9\rangle\) in \(\mathbf{i}, \mathbf{j}\) form is \(\boxed{6\mathbf{i}-9\mathbf{j}}\).