If ` vec c` is perpendicular to both ` vec a\ a n d\ vec b ,` then prove that it is perpendicular to both ` vec a+ vec b\ a n d\ vec a- vec bdot`

Explanation

It is given that `vec c` is perpendicular to both ` vec a\ a n d\ vec b ,`
Therefore,
` vec c * vec a=0` and ` vec c * vec b=0`
Now we have to show , `vec c *( vec a+ vec b)=0`
`=>vec c *( vec a+ vec b)= vec c* vec a+ vec c* vec b`
`=>vec c *( vec a+ vec b)= 0+0`
`=>vec c *( vec a+ vec b)=0`
Hence `vec c` is perpendicular to `( vec a+ vec b)`
similarly,
we have to show , `vec c *( vec a- vec b)=0`
`=>vec c *( vec a- vec b)= vec c* vec a- vec c* vec b`
`=>vec c *( vec a- vec b)= 0-0`
`=>vec c *( vec a- vec b)=0`
Hence `vec c` is perpendicular to `( vec a- vec b)`