Let a plane P pass through the point (3, 7, -7) and contain the line, x - 2 / - 3 = y - 3 / 2 = z + 2 / 1. If distance of the plane P from the origin is d, then d^(2) is equal to ______________.

->BA = hat i + 4hat j - 5hat k \ ->BA x vec l = vec n = hat i hat j hat k \ -3 2 1 \ 1 4 -5 \ ahat i + bhat j + chat k = -14hat i - 14hat j - 14hat k \ => a = 1, b = 1, c = 1 \ Plane: (x - 2) + (y - 3) + (z + 2) = 0 \ => x + y + z - 3 = 0 \ Therefore d = sqrt(3) implies d^2 = 3 \

Let a plane P pass through the point 3 7 7 and contain ... | null (Mathematics)

\begin{aligned} \overrightarrow{BA} &= \hat{i} + 4\hat{j} - 5\hat{k} \\ \overrightarrow{BA} \times \vec{l} &= \vec{n} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ -3 & 2 & 1 \\ 1 & 4 & -5 \end{vmatrix} \\ a\hat{i} + b\hat{j} + c\hat{k} &= -14\hat{i} - 14\hat{j} - 14\hat{k} \\ \Rightarrow \quad & a = 1, \ b = 1, \ c = 1 \\ \text{Plane:} \quad & (x - 2) + (y - 3) + (z + 2) = 0 \\ \Rightarrow \quad & x + y + z - 3 = 0 \\ \therefore \quad & d = \sqrt{3} \implies d^2 = 3 \end{aligned}

Explanation

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