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If vec(a)=-vec(b), then |vec(a)|=|vec(b)...

If `vec(a)=-vec(b)`, then `|vec(a)|=|vec(b)|` .

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If |vec(a)|=|vec(b)| , then vec(a)=vec(b) .

If vec(a)=vec(b)+vec(c ) , then |vec(a)|=|vec(b)+vec(c )| .

Knowledge Check

  • Consider the following inequalities in respect of vector vec(a) and vec(b) 1. |vec(a) + vec(b)| le |vec(a)| + |vec(b)| 2. |vec(a) - vec(b)| ge |vec(a)|- |vec(b)| Which of the above is/are correct?

    A
    A) Only 1
    B
    B) Only 2
    C
    C) Both 1 and 2
    D
    D) Neither 1 nor 2

  • For non-zero vectors vec(a)andvec(b)if|vec(a)+vec(b)|lt|vec(a)-vec(b)|,"then "vec(a)andvec(b) are

    A
    collinear
    B
    perpendicular to each other
    C
    inclined at an acute angle
    D
    inclined at an obtuse angle

  • Consider the following inequalities in respect of vectors vec(a) and vec(b) : 1. |vec(a)+vec(b)| £|vec(a)|+|vec(b)| 2. |vec(a)-vec(b)|3|vec(a)|-|vec(b)| Which of the above is/are correct ?

    A
    1 only
    B
    2 only
    C
    Both 1 and 2
    D
    Neither 1 nor 2

    • Similar Questions

    Explore conceptually related problems

    Prove that |vec(a)|-|vec(b)|le |vec(a)-vec(b)| .

    Establish the following vector in equalities: (i) |vec(a)-vec(b)| le |vec(a)| +|vec(b)| (ii) |vec(a) -vec(b)| ge |vec(a)| - |vec(b)| What does the equality sign apply ?

    (a) What is the geometric significance of the relation |vec(a)+vec(b)|=|vec(a)-vec(b)| ? (b) Prove geometrically that |vec(a)+vec(b)|le |vec(a)|+|vec(b)| .

    The inequality |vec(a).vec(b)|le |vec(a)||vec(b)| is called :

    Let |vec(a)| # 0.|vec(b)| ne 0 (vec(a) + vec(b)). (vec(a) + vec(b)) = |vec(a)|^(2) + |vec(b)|^(2) holds if and only if

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