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A : Angle between the vectors I - 2j + k...

A : Angle between the vectors I - 2j + k, 2i - j - k is `(pi)/(3)`.
R : If `theta` is the angle between a,b then cos `theta = (a.b)/(|a||b|)`

A

both A and R are true and R is the correct explanation of A

B

Both A and R are true but R is not correct explanation of A

C

A is true but R is false

D

A is false but R is true

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • The angle between the vectors (i + j + k) and (i- j - k) is

    A
    `"sin"^(-1) (sqrt8)/(3)`
    B
    `cos^(-1) ((2)/(3))`
    C
    `"cos"^(-1) (sqrt8)/(3)`
    D
    `sin^(-1) ((8)/(9))`

  • If theta is the angle between the unit vectors a,b then |a + b| =

    A
    sin `(theta //2)`
    B
    2 sin `(theta // 2)`
    C
    cos `(theta // 2)`
    D
    2 Cos `(theta // 2)`

  • The sine of the angle between the vectors I + 3j - 2k, 2i - 4j - k is

    A
    `3//4`
    B
    `3//5`
    C
    `5//6`
    D
    `5//7`

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    Find the angle between the vectors (-2i + 2j) and 3i

    The vectors 2i - 3j + k, I - 2j + 3k, 3i + j - 2k

    If theta is th angle between the vector 2i - 2j + 4k and 3i + j + 2k, then sin theta =

    {:(I."The angle between the vectors" 2i. + j- k I - 4j - 2k, a. pi//6),(II. "The angle between the vectors" I + 2j - k 2i + j + k, b. pi//4),(III. "The angle between a.b if a.b if a.b.a + b are unit vector",c. pi//3),(IV. "The angle between" vec(AC) vec(BD) if A = (1.1.0) B = (1. -1.0) C = (-1.1.0) D = (0.-1.1),d.pi//2):}

    If P = 2i + 3j - 4k and Q = 5i + 2j + 4k find the angle between the two vectors

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