Question

p(1 0 -2) q(3 -2 0) the diruction cosin of pq is​

Answer 1

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Class 12

>>Maths

>>Vector Algebra

>>Introduction to Vectors

>>Find the direction cosines ...

Question

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Find the direction cosines of the vector joining the points P(1,2,−3) and Q(−1,−2,1), which is directed from P to Q.

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Solution

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Correct option is

A

(−

3

1

,−

3

2

,

3

2

)

Given,

OP

=1

i

^

+2

j

^

−3

k

^

and

OQ

=−1

i

^

−2

j

^

+1

k

^

,

where O is the origin.

Now,

PQ

=

OQ

−

OP

=(−1−1)

I

^

+(−2−2)

j

^

+(1−(−3))

k

^

=−2

i

^

−4

j

^

+4

k

^

∣

PQ

∣=

(−2)

2

+(−4)

2

+(4)

2

=6

Unit vector in the direction of

PQ

is,

PQ

^

=

∣

PQ∣

PQ

=

6

−2

i

^

−4

j

^

+4

k

^

=−

3

1

i

^

−

3

2

j

^

+

3

2

k

^

Hence direction cosines are (

3

−1

,

3

−2

,

3

2

)