1
Question
Find the equation of a line passing through the point (1,2,−4) and perpendicular to two lines →r=(8^i−19^j+10^k)+λ(3^i−16^j+7^k) and →r=(15^i+29^j+5^k)+μ(3^i+8^j−5^k).
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Solution
The required line is
parallel to a vector which is obtained by the cross product of the vectors to
which the given lines are parallel.
Thus the required vector is:
∣∣
∣
∣∣^i^j^k3−16738−5∣∣
∣
∣∣=24^i+36^j+72^k
Now since the line has
to pass through the point ^i+2^j−4^k, its
equation is →r=(^i+2^j−4^k)+γ(24^i+36^j+72^k).
The required line is parallel to a vector which is obtained by the cross product of the vectors to which the given lines are parallel.
Thus the required vector is:
∣∣ ∣ ∣∣^i^j^k3−16738−5∣∣ ∣ ∣∣=24^i+36^j+72^k
Now since the line has to pass through the point ^i+2^j−4^k, its equation is →r=(^i+2^j−4^k)+γ(24^i+36^j+72^k).
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