Combinations of Lines & Planes (Edexcel A-Level Further Mathematics): Quizzes

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Combinations of Lines & Planes
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In the line equation r=a+λb\mathbf{r} = \mathbf{a} + \lambda \mathbf{b}, what does b\mathbf{b} represent?

Direction vector of the line

What does n\mathbf{n} represent in the plane equation?

Normal vector to the plane

What is the first step to find the intersection of a line and a plane?

Substitute line equation into plane eq

After finding λ\lambda, what is the next step to find the intersection point?

Substitute λ\lambda into line equation

In the perpendicular distance formula, what is the numerator?

∣ax1+by1+cz1+d∣|ax_1 + by_1 + cz_1 + d|

In the perpendicular distance formula, what is the denominator?

a2+b2+c2\sqrt{a^2 + b^2 + c^2}

What is the Cartesian form of a plane equation?

ax+by+cz+d=0ax + by + cz + d = 0

In the worked example, what is the value of λ\lambda?

115\frac{1}{15}

In the worked example, what does the equation simplify to after substitution?

15λ+9=1015\lambda + 9 = 10

In the worked example, what is the xx-coordinate of the intersection point?

1915\frac{19}{15}

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