Find a vector of magnitude 49, which is perpendicular to both the vectors `2 hat i+3 hat j+6 hat k\ a n d\ 3 hat i-6 hat j+2 hat kdot`

Explanation

We have given

`vec{a}=2 hat i+3 hat j+6 hat k` and
`vec{b}= 3 hat i-6 hat j+2 hat k`
` therefore vec{a} times vec{b}=|hat{i}\ hat{j} \ hat{k}\ 2 3\ 6\ 3\ -6\ 2| `

`=(6+36) hat{i}-(4-18) hat{j}+(-12-9) hat{k}`

`=42 hat{i}+14 hat{j}-21 hat{k}`

`Rightarrow|vec{a} times vec{b}|=sqrt{42^{2}+14^{2}+(-21^{2})}`

`=sqrt{2401}`

`=49`

Required vector `=49 times{frac{vec{a} times vec{b}}{|vec{a} times vec{b}|}}`

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