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If a unit vector is represented by...

If a unit vector is represented by `0.5 hati + 0.8 hatj + c hatk` ,the value of c is

A

`sqrt0.89`

B

`0.2`

C

`0.3`

D

`sqrt0.11`

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • IF a is a unit vector , then | a xx hati |^2 +| a x hatj |^2 | |a xx hatk |^2 =

    A
    2
    B
    4
    C
    1
    D
    0

  • If a, b, c are distinct real numbers and P, Q, R are three points whose position vectors are respectively ahati + b hatj + c hatk , b hati + c hatJ + a hatk and c hai + a hatj + b hatk , then angle QPR =

    A
    `cos^(-1) (a +b+ c)`
    B
    `pi/2`
    C
    `pi/3`
    D
    `cos^(-1) ( (a^2 + b^2 + c^2) /(abc) ) `

  • If e is unity vector perpendicular to the plane determined by the points 2hati + hatj + hatk , hati - hatj + hatk - hatj + hatk and - hati + hatj - hatk . If a = 2 hati -3 hatj + 6 hatk , then the projection vector of a on e is

    A
    `11/14 ( - 2 hati + hatj + 3 hatk) `
    B
    `1/3 (hati - 2hatj+ 2hatk)`
    C
    `1/7 (2hati - 3hatj + 6hatk)`
    D
    `(1)/(sqrt14) (2 hati - hatj + 3 hatk)`

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