What is the scalar product of -2i+3j+4k and 5i-3j+3k, where I, j and k are the Cartesian unit vectors? answers given A,-15. B,-10. C, -7. D, 7. E, 10. ?

1 Answer
Aug 14, 2018

$\vec{a} \cdot \vec{b} = - 7 \to C$

Explanation:

We know that,

$\text{If } \vec{x} = \left({x}_{1} , {x}_{2} , {x}_{3}\right) \mathmr{and} \vec{y} = \left({y}_{1} , {y}_{2} , {y}_{3}\right) ,$

$\text{then scalar(dot) product of } \vec{x} \mathmr{and} \vec{y}$ is :

color(red)(vecx*vecy=x_1y_1+x_2y_2+x_3y_3.

Let

$\vec{a} = - 2 i + 3 j + 4 k = < - 2 , 3 , 4 >$

$\vec{b} = 5 i - 3 j + 3 k = < 5 , - 3 , 3 >$

$\therefore \vec{a} \cdot \vec{b} = < - 2 , 3 , 4 > \cdot < 5 , - 3 , 3 >$

$\therefore \vec{a} \cdot \vec{b} = \left(- 2\right) \left(5\right) + \left(3\right) \left(- 3\right) + \left(4\right) \left(3\right)$

$\therefore \vec{a} \cdot \vec{b} = - 10 - 9 + 12$

$\therefore \vec{a} \cdot \vec{b} = - 7$