Question

ifa vector equals to ICAP + 3 J cap + 2 k cap and b vector equals to 3 ICAP + 2 J cap + 2 k cap find the vector product a vector into b vector ​

Answer 1

Answer:

the answer is 4i+5j+4k

Answer 2

The vector product of given vectors are  $c= 2i+4j-7k$

Cross Product definition:

• Cross product between any two vectors will determine the area between those vectors.
• The multiplication sign that is × is placed between two vectors to denote a cross product.

• As the outcome of the cross product of vectors is a vector quantity, the cross product of two vectors is also known as a vector product.

Cross Product Formula:

$c=$$a$×$b=$ $|a| |b| sin\alpha$

where $|a|=$ magnitude of vector $a$

$|b|=$ magnitude of vector $b$

$\alpha =$ angle between $a$ and $b$ vectors.

$a= a_{1} i + a_{2} j + a_{3} k$

$b = b_{1}i + b_{2}j + b_{3}k$

Cross product of two the vector is done through matrix:

vectors given :

$a = i + 3j +2k$ and $b = 3i + 2j + 2k$

∴ $c = a$×$b$

$c = \left[\begin{array}{ccc}i&j&k\\1&3&2\\3&2&2\end{array}\right]$

$c= i(a_{2} b_{3} -a_{3} b_{2} ) -j (a_{1} b_{3} -a_{3} b_{2} )+k (a_{1} b_{2} -a_{2} b_{1} )$

Putting the values:

$c= i(6-4) - j (2-6) +k (2-9)\\c= 2i+4j-7k$

Hence, the vector product of given vectors are $c= 2i+4j-7k$