Question

vector is equal to ICAP + 2 J cap + 3 k cap if vector b is equal to 3 ICAP + 2 J cap + 2 k cap find vector a into
vector b is equal to​

Answer 1

Explanation:

Let the vectors be A and B.

Given, A= i + 2j + 3k and B= 3i + 2j + 2k

We can find product of vectors in two ways

I. FINDING VECTOR/CROSS PRODUCT:

Using multiplication of vectors by matrix,

A × B= $\left[\begin{array}{ccc}i&j&k\\1&2&3\\3&2&2\end{array}\right]$= [(2x2)-(3x2)] i + [(1x2)-(3x3)] j + [(1x2)-(2x3)] k

A × B= [4-6] i + [2-9] j + [2-6] k =  –2 i – 7 j – 4 k

∴ Vector product of vectors A and B = -2i - 7 j - 4 k

II. FINDING SCALAR/DOT PRODUCT:

A · B = (1X3)i + (2X2)j + (3X2)k = 3i + 4j + 6k

∴ Scalar product of vectors A and B = 3i + 4j + 6k