If the points A(1,0,−4),B(−1,p,q) and C(−3,7,4) are collinear,find the values of p and q
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Solution
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Given that the points A(1,0,−4),B(−1,p,q) and C(−3,7,4) are collinear.Let the point B divide the line segment AC in the ratio k:1, then by section formula the coordinates of the point B are
(−3k+1k+1,7k+0k+1,4k−4k+1)
But the coordinates of the point B are (−1,p,q), so we have,
−3k+1k+1=−1,7kk+1=p,4k−4k+1=q
⇒−3k+1=−k−1,7kk+1=p,4k−4k+1=q
⇒−3k+k=−1−1,7kk+1=p,4k−4k+1=q
⇒−2k=−2,7kk+1=p,4k−4k+1=q
⇒k=1,7×11+1=p,4×1−41+1=q
⇒k=1,72=p,02=q
∴k=1,p=72,q=0
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