Show that the line joining the origin to the point $(2, 1, 1)$ to perpendicular to the line determined by the points $(3, 5, - 1), (4, 3, - 1)$

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Solution

$_{1} \Rightarrow 2^i +^j +^k$
$_{1} \Rightarrow (4 - 3)^I + (3 - 5)^J + (- 1 + 1)^k$
$=^i - 2^j$
$_{1} ._{2} = (2^i +^j +^k) . (^i - 2^j)$
$= 2 - 2$
$= 0$
$∴_{1}$ is $⊥ r$ to $_{2}$

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Show that the line joining the origin to the point (2,1,1) to perpendicular to the line determined by the points (3,5,−1),(4,3,−1)

→l1 ⇒ 2^i+^j+^k→l1 ⇒ (4−3)^I+(3−5)^J+(−1+1)^k=^i−2^j→l1.→l2=(2^i+^j+^k).(^i−2^j)=2−2=0∴ →l1 is ⊥r to →l2

Show that the line joining the origin to the point $(2, 1, 1)$ to perpendicular to the line determined by the points $(3, 5, - 1), (4, 3, - 1)$

$_{1} \Rightarrow 2^i +^j +^k$
$_{1} \Rightarrow (4 - 3)^I + (3 - 5)^J + (- 1 + 1)^k$
$=^i - 2^j$
$_{1} ._{2} = (2^i +^j +^k) . (^i - 2^j)$
$= 2 - 2$
$= 0$
$∴_{1}$ is $⊥ r$ to $_{2}$