given A=4i-10j and B= 7i+5j find b such that A+bB is a vector pointing along the x-axis (i. e has no y component)​

-4/7

Explanation:

Given the following

A=4i-10j and B= 7i+5j

A+ bB = 4i-10j + (7i+5j)b

A+ bB =  4i-10j + 7ib+5jb

A+ bB =

The vector along the x-axis is expressed as i + 0j

If the vector A+ bB is pointing in the direction of the x-axis then;

Hence the value of b is -4/7

The value of such that is 2.

According to the statement, we have following system of vectorial equations:

(1)

(2)

(3)

By applying (1) and (2) in (3):

And we get two scalar equations after analyzing each component:

(4)

(5)

We solve for in (5):

And for in (4):

The value of such that is 2.

Please see this question related to Sum of Vectors for further details:

would be false hope this out

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