Question

Two vectors are given by A=3i+4j and B=2i-5j calculate their dot and cross product?

Answer 1

Answer:

A.B = -14

A x B=-23 k

Explanation:

Important Equalities :

$i.i=1,i\times i=0\\ \\ i.j=0, i \times j=k,j\times i=-k$

1) We have,

$A=3i+4j\\ \\B=2i-5j$

Then,

$A.B = (3i+4j).(2i-5j)=3*2+4*-5\\ \\=6-20=-14$

Hence, Dot Product  is -14 (Scalar)

2) Now,

$A \times B=(3i+4j)\times (2i-5j)\\ \\=3i\times2i+3i\times-5j+4j\times2i+4j\times-5j\\ \\=0-15k-8k=-23k$

Hence, Vector Product is -23 k (Vector)

Answer 2

Answer:

Explanation:Dot product:

A*B=(multiplying the same vectors..i*iand j*j)

3i * 2i =6i

4j * -5j= -20j

Hence=6-20= -14

Cross product:

A*B =3*2+3*-5+4*2+4*-5= -23k