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If l(1), m(1), n(1) and l(2), m(2), n(2)...

If `l_(1), m_(1), n_(1)` and `l_(2), m_(2), n_(2)` are the direction cosines of two vectors and `theta` is the angle between them, then the value of cos `theta` is

A

`l_(1)l_(2) + m_(1)m_(2) + n_(1)n_(2)`

B

`l_(1)m_(1) + m_(1)n_(1) + n_(1)l_(1)`

C

`l_(2)m_(2)+m_(2)n_(2) + n_(2)l_(2)`

D

`m_(1)l_(2) + l_(2)m_(2) + n_(1)m_(2)`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • If (l_(1), m_(1), n_(1)), (l_(2), m_(2), n_(2)) are the direction cosines of two perpendicular lines and theta is the angle made by one of the bisectors of the angle between the lines with the positive direction of the x-axis then

    A
    `sin theta=l_(1)-l_(2)`
    B
    `cos theta=(l_(1)-l_(2))/(2)`
    C
    `sin theta =sqrt(2)(l_(1)-l_(2))`
    D
    `cos theta=((l_(1)+l_(2)))/(sqrt(2))`

  • If (l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)) are direction cosines of two lines which inculude an angle 120^(@) , then the direction cosines of the line which bisects the angle between them is

    A
    `(l_(1)+l_(2)),(m_(1)+m_(2)),(n_(1)+n_(2))`
    B
    ` ((l_(1)-l_(2))/(sqrt(3)),(m_(1)-m_(2))/(sqrt(3)),(n_(1)-n_(2))/(sqrt(3)))`
    C
    ` ((l_(1)-l_(2))/(2),(m_(1)-m_(2))/(2),(n_(1)-n_(2))/(2))`
    D
    ` ((l_(1)-l_(2))/(sqrt(2)),(m_(1)-m_(2))/(sqrt(2)),(n_(1)-n_(2))/(sqrt2))`

  • If the two directional cosines of a vectors are 1/sqrt(2) and 1/sqrt(3) then the value of third directional cosine is

    A
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    B
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    C
    `1/sqrt(7)`
    D
    `1/sqrt(10)`

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