Vectors ` vec a\ a n d\ vec b` are inclined at angel `theta=120^0` . If `| vec a|=1,\ | vec b|=2,\ ` then `[( vec a+3 vec b)xx(3 vec a- vec b)]^2` is equal to `300` b. `235` c. `275` d. 225

Explanation

`(\vec{a}+3 \vec{b}) \times(3 \vec{a}-\vec{b}) `

`=3(\vec{a} \times \vec{a})-\vec{a} \times \vec{b}+9(\vec{b} \times \vec{a})-3(\vec{b} \times \vec{b}) `

`=3(0)-\vec{a} \times \vec{b}-9(\vec{a} \times \vec{b})-3(0) `

`=-10(\vec{a} \times \vec{b}) `

`\text { Now } `

`|(\vec{a} \times 3 \vec{b}) \times(3 \vec{a}-\vec{b})|^{2} `


`=|-10(\vec{a} \times \vec{b})|^{2} `

`=100|(\vec{a} \times \vec{b})|^{2} `

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