1.

If u=a-b and v=a+b and |a|=|b|=2, then |uxx v| is equal to

Answer»

`2sqrt(16-(a.b)^(2))`
`sqrt(16-(a.b)^(2))`
`2sqrt(4-(a.b)^(2))`
`2sqrt(4+(a.b)^(2))`

Solution :Now, `|uxxv|=(a-b)XX(a+b)=2|=2||AXXB|`
`[because axxa =bxxb=0]`
and `|axxb|^(2)+(a*b)^(2)=(ab SIN theta)^(2)+(ab cos theta)^(2)=a^(2)b^(2)`
`|axxb|=sqrt(a^(2)b^(2)-(a*b)^(2))`
So`|uxxv|=2|axxb|=2sqrt(a^(2)b^(2)-(a*b)^(2))`
`=2sqrt(2^(2)2^(2)-(a*b)^(2))`
`=2sqrt(16-(a*b)^(2))[because |a|=|b|=2]`


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