Given \(\vec a=\hat i+4\hat j + 2\hat k,\) \(\vec b=3\hat i-2\hat j+7\hat k\) and \(\vec c=2\hat i-\hat j+4\hat k\)
We need to find a vector \(\vec d\) perpendicular to \(\vec a\) and \(\vec b\) such that \(\vec c.\vec d=15.\)
Recall a vector that is perpendicular to two vectors
Here, we have (a1, a2, a3) = (1, 4, 2) and (b1, b2, b3) = (3, –2, 7)
So, \(\vec d\) is a vector parallel to \(\vec a\times\vec b\).