\(\displaystyle{F}_{{B}}={q}{v}\times{B}\) is the equation to use: in words, v "crosses" B

\(\displaystyle\therefore\) in vector notation (instead of unit vector notation) \(\displaystyle{\frac{{{b}}}{{{c}}}}\) it's the same and its easier for me to type in:

a) \(\displaystyle{F}_{{B}}={q}{v}\times{B}\)

\(\displaystyle={q}{\left({<}{2000000}{i},{3}{000}{000}{j}{>}{x}{<}{0.03}{i},-{0.15}{j}{>}\right)}\)

\(\displaystyle={q}{\left(-{390000}{k}\right)}\)

\(\displaystyle={\left(-{1.602}\times{10}^{{{19}}}\right)}{\left(-{390000}{k}\right)}\)

\(\displaystyle={6.25}\times{10}^{{-{14}}}{N}\)

b) \(\displaystyle{F}_{{B}}={q}{v}\times{B}\)

\(\displaystyle={q}{\left({<}{2}{000000}{i},{3000000}{j}{>}{x}{<}{0.03}{i},-{0.15}{j}{>}\right)}\)

\(\displaystyle={\left(+{1.602}\times{10}^{{{19}}}\right)}{\left(-{390000}{k}\right)}\)

\(\displaystyle=-{6.25}\times{10}^{{-{14}}}{N}\)

pointed into the plane

As the texbook points out, answers are correct.

\(\displaystyle\therefore\) in vector notation (instead of unit vector notation) \(\displaystyle{\frac{{{b}}}{{{c}}}}\) it's the same and its easier for me to type in:

a) \(\displaystyle{F}_{{B}}={q}{v}\times{B}\)

\(\displaystyle={q}{\left({<}{2000000}{i},{3}{000}{000}{j}{>}{x}{<}{0.03}{i},-{0.15}{j}{>}\right)}\)

\(\displaystyle={q}{\left(-{390000}{k}\right)}\)

\(\displaystyle={\left(-{1.602}\times{10}^{{{19}}}\right)}{\left(-{390000}{k}\right)}\)

\(\displaystyle={6.25}\times{10}^{{-{14}}}{N}\)

b) \(\displaystyle{F}_{{B}}={q}{v}\times{B}\)

\(\displaystyle={q}{\left({<}{2}{000000}{i},{3000000}{j}{>}{x}{<}{0.03}{i},-{0.15}{j}{>}\right)}\)

\(\displaystyle={\left(+{1.602}\times{10}^{{{19}}}\right)}{\left(-{390000}{k}\right)}\)

\(\displaystyle=-{6.25}\times{10}^{{-{14}}}{N}\)

pointed into the plane

As the texbook points out, answers are correct.