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For tow vectros vec A and vec B | ve...

For tow vectros ` vec A` and `vec B`
` | vec A + vec B| = | vec A- vec B|` is always true when.

A

`|vecA|=|vecB|ne0`

B

`vecA bot vecB`

C

`|vecA|=|vecB|ne 0 and vecA and vecB` are parallel or antiparallel

D

when either `|vecA| or| vecB|` is zero

Text Solution

Verified by Experts

The correct Answer is:
B, D
(b,d): Given `|vecA+vecB|=|vecA-vecB|`
or `sqrt(|vecA|^(2)+|vecB|^(2)+2|vecA|vecB|cos theta)`
`=sqrt(|vecA^(2)|+|vecB|^(2)-2|vecA|vecB|cos theta)`
or `4|vecA|vecB|cos theta=0`
Here, `|vecA|ne0 "or" |vecB|ne0`, therefore, `cos theta =0`
i.e. `theta=90^(@)`
which implies that `vecA _|_ vecB.` When either `|vecA|` or `|vecB|` is 0 then `|vecA|vecB|=|vecA-vecB|`
The correct options are (b) and (c).
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