Question

if vector a is equal to two ICAP - 2 J cap + K cap and vector B equal to minus 3 i cap + 4 j cap - 2 k cap find vector a b and vector a cross vector b​

Answer 1

Answer:

vector $a.b=-16 units$

vector a cross vector b​ =  $2K+7j$

Explanation:

(i)vector $a.b$

        $=(2i-2j+k)(-3i+4j-2k)$

        $=-6-8-2$

        $=-16 units$

(ii) vector a cross vector b

         $=(2i-2j+3k)$ ×  $(-3i+4j-2k)$

         $=8k+4j-6k+4i+3j-4i$

          $=2k+7j$

#SPJ3

Answer 2

Answer:

The dot products of the two vectors a.b=$16$ units
The cross product of the two vectors $aXb$ = $2k + 7j$

Explanation:

• The dot product of two vectors is simply the multiplication of the two vectors where $i*i=j*j=k*k=1$ and $i*j=j*k=i*k=0$
  hence
  $a.b = (2i-2j+k) * (-3i+4j-2k)$
  $a.b = 16$ units
• The cross vector or vector product is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space.
  Hence
  $\left[\begin{array}{ccc}i&j&k\\2&-2&3\\-3&4&2\end{array}\right]$
  After solving the determinant we get the cross product as
  $aXb=2k + 7j$
  #SPJ2