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The value of a.b where a = 2i - 3j -k, b...

The value of a.b where a = 2i - 3j -k, b = 3i + 2j - 2k

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Knowledge Check

  • The ascending order of the following (A) volume of the tertrahedron formed by 4i + 5j + k. - j + k. 3i + 9j + 4k, -4i + 4j + 4k (B) Volume of the parallelopiped with edges 2i + 3j + 4k. I + 2j - 2k, 3i - j + k (C ) |a xx (b xx c)| where a = 2i + 3j - 4k, b = i j + k, c = 4i + 2j + 3k (D) |(a xx b) xx c| where a = i - 2j + k, b = 2i + j - k, c = 4i + 2j + 3k

    A
    A,B,C,D
    B
    A,D,B,C
    C
    A,C,B,D
    D
    C,B,A,D

  • A unit vector perpendicular to the plane of a = 2i - 6j -3k, b = 4i + 3j - k is

    A
    `(4i + 3j - k)/(sqrt(26))`
    B
    `(2i - 6j - 3k)/(7)`
    C
    `(3i - 2j + 6k)/(7)`
    D
    `(2i - 3j - 6k)/(7)`

  • The unit vector orthogonal to a = 2i + 2j + k, b = 3i + 4j - 12k and forming a right handed system with a and b is

    A
    28i - 27j - 2k
    B
    `-28i + 27j + 2k`
    C
    `(28i - 27j - 2k)/(sqrt(1517))`
    D
    `(-28i + 27j + 2k)/(sqrt(1517))`

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    I : If a = 3i - 2j + k, b = 2i - 4j - 3k, c = -i + 2j + 2k then a + b + c = 4i + 4j II : If a = i - j + 2k, b = 2i + 3j + k, c = i - k, then magnitude of a + 2b - 3c is sqrt(78)

    If a = 2i - j + k, b = 3i + 4j - k then |a xx b| =

    If a = 3i - 2j + k, b = 2i - 4j - 3k, c = -i + 2j + 2k then a + b + c =

    {:(I."If" a = 2i - 3j -k. b = i + 4j - 2k "then" (a + b) xx (a - b), a. 42 i + 14 j - 21 k),(II. "If" a = 3i - j - 2k. b - 2i + 3j + k "then" (a + 2b) xx (2a - b), b. -5i + 5j + 5k),(III. "If" a = i + 2j - 3k. b = 2i + j + k "then" a xx b, c. -25i + 35j - 55 k),(IV. "If" a = 2i + 3j + 6k. b = 3i - 6j + 2k "then" a xx b, d. -20i - 6j - 22k):}

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

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