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प्रश्न
If `veca and vecb` are perpendicular vectors, `|veca+vecb| = 13 and |veca| = 5` ,find the value of `|vecb|.`
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उत्तर
Given that `veca and vecb` are two perpendicular vectors.
Thus, ` veca .vecb= 0 `
Also given that, ` |veca +vecb| 13 and |veca|=5.`
We need to find the value of vecb.
Consider `|veca + vecb|^2 :`
`|veca +vecb|^2 = |veca|^2 |veca.vecb|+|vecb|^2`
`13^2=5^2+2xx0+|vecb|^2`
`169=25+|vecb|^2`
`|vecb|^2=169-25`
`|vecb|^2=144`
`vecb=12`
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