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If a and b are two non-zero and non-coll...

If a and b are two non-zero and non-collinear vectors then a+b and a-b are

A

linearly dependent vectors

B

linearly independent vectors

C

linearly dependent annd independent vectors

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Since, a and b are non-collinear, so a+b and a-b will also be non-collinear.
Hence, a+b and a-b are linearly independent vectors.
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Knowledge Check

  • If vec a and vec b are two non zero and different vectors such that |vec a + vec b| = |vec b - vec a| , then the angle between the vectors vec a and vec b is

    A
    `pi/3`
    B
    `pi/4`
    C
    `pi/2`
    D
    `pi/6`

  • Let vec a and vec b be two non collinear unit vectors. If vec u = vec a - (vec a . vec b) vec b and vec nu = vec a xx vec b , then |vec nu| =

    A
    `|vec u|`
    B
    `|vec u| + |vec nu . vec a|`
    C
    `2|vec nu|`
    D
    `|vec u|+vec u.(vec a + vec b)`

  • If vec a, vec b, vec c non zero coplanar vectors, then, [2 vec a - vec b 3 vec b - vec c 4 vec c - vec a] =

    A
    9
    B
    27
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