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If the vectors hati-hatj, hatj+hatk and ...

If the vectors `hati-hatj, hatj+hatk and veca` form a triangle then `veca` may be (A) `-hati-hatk` (B) `hati-2hatj-hatk` (C) `2hati+hatj+hatjk` (D) hati+hatk`

A

`-hati-hatk`

B

`hati-2hatj-hatk`

C

`2hatj+hatj+hatk`

D

`hati+hatk`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
`a=[+-(hati-hatj)+-(hatj+hatk)]`
`=+-(hati+hatk),+-(hati-2hatj-hatk)`
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The vectors which is/are coplanar with vectors hati+hatj+2hatk and hati+2hatj+hatk and perpendicular to the vector hati+hatj+hatk is /are (A) hatj-hatk (B) -hati+hatj (C) hati-hatj (D) -hatj+hatk

Vectors perpendicular to hati-hatj-hatk and in the plane of hati+hatj+hatk and -hati+hatj+hatk are (A) hati+hatk (B) 2hati+hatj+hatk (C) 3hati+2hatj+hatk (D) -4hati-2hatj-2hatk

Knowledge Check

  • [hati hatk hatj]+[hatk hatj hati]+[hatj hatk hati] is equal to

    A
    1
    B
    3
    C
    `-3`
    D
    `-1`

  • The three vectors vecA=3hati-2hatj+hatk, vecB=hati-3hatj+5hatk and vecC=2hati+hatj-4hatk form

    A
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    B
    Isosceles triangle
    C
    A right angled triangle
    D
    No triangle

  • If the vectors of a trianlge are A(hati+hatj+2hatk), B(3hati-hatj+2hati) and C(2hati-hatj+hatk) the area of triangle is

    A
    `2sqrt3` sq units
    B
    `sqrt3` sq units
    C
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    D
    3 sq units

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    The vector (s) equally inclined to the vectors hati-hatj+hatk and hati+hatj-hatk in the plane containing them is (are_ (A) (hati+hatj+hatk)/sqrt(3) (B) hati (C) hati+hatk (D) hati-hatk

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