Let P = (x_1, y_1, z_1) and Q = (x_2, y_2, z_ | vedclass

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(B) The projection of a line segment joining two points $P(x_1, y_1, z_1)$ and $Q(x_2, y_2, z_2)$ on a line with direction cosines $l, m, n$ is given

Vedclass · Accepted Answer

$\left[ l(x_2 - x_1) + m(y_2 - y_1) + n(z_2 - z_1) \right]$

Vedclass · Answer

(B) The projection of a line segment joining two points $P(x_1, y_1, z_1)$ and $Q(x_2, y_2, z_2)$ on a line with direction cosines $l, m, n$ is given by the formula: Projection = $l(x_2 - x_1) + m(y_2 - y_1) + n(z_2 - z_1)$. This is derived from the dot product of the vector $\vec{PQ} = (x_2 - x_1)\hat{i} + (y_2 - y_1)\hat{j} + (z_2 - z_1)\hat{k}$ and the unit vector along the line $AB$,which is $\hat{u} = l\hat{i} + m\hat{j} + n\hat{k}$. Thus,the projection is $\vec{PQ} \cdot \hat{u} = l(x_2 - x_1) + m(y_2 - y_1) + n(z_2 - z_1)$.

Let $P = (x_1, y_1, z_1)$ and $Q = (x_2, y_2, z_2)$ be two points. If the direction cosines of a line $AB$ are $l, m, n$,then the projection of the line segment $PQ$ on the line $AB$ is:

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