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Manipal Entrance Test 2019 Math Paper

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Question : 29 of 70

Marks: +1, -0

If

(3,4,5), Q(4,6,3), R(-1,2,4), S(1,0,5),

then the projection of

R S

P Q

is

$-\frac{2}{3}$
$-\frac{4}{3}$
$\frac{1}{2}$
$2$

Solution:

We have,

P(3,4,5), Q(4,6,3), R(-1,2,4)

and

S(1,0,5)

Direction ratios of

P Q

are (1,2,-2) and direction cosines of

P Q

are

\frac{1}{\sqrt{1^{2}+2^{2}+(-2)^{2}}}

,

\frac{2}{\sqrt{1^{2}+2^{2}+(-2)^{2}}},

\frac{-2}{\sqrt{1^{2}+2^{2}+(-2)^{2}}}

=\frac{1}{\sqrt{9}},\frac{2}{\sqrt{9}},\frac{-2}{\sqrt{9}}

=\frac{1}{3},\frac{2}{3},-\frac{2}{3}

∴ Required projection of

R S

on

P Q

is

l (x_{2}-x_{1})+m(y_{2}-y_{1})+n(z_{2}-z_{1})

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