Given vectors a = xˆ2−yˆ +zˆ3 and b = xˆ3−zˆ2, find a vector c whose magnitude is 9 and whose direction is perpendicular to both a and b

Vector C = 1.334i + 8.671j + 2k or 1.334x + 8.671y + 2z

Explanation:

The concept applied to solve the question is cross product of vector, AXB since vector C is perpendicular to vector A and B and this is solved by applying the 3X3 determinant method.

A detailed step by step explanation is attached below.

and

Explanation:

Let's write the vectors A,B and C:

Now, let's remember when two vector are perpendicular, the scalar product between them is 0. Then, using this concept, we have:

(1)

(2)

Also we know that magnitude of C must be 9, so:

(3)

Let's solve the equation (2) for a:

(4)

Let's put (4) on equation (1), and solve it for b:

(5)

Let's put (4) and (5) in (3) and find c.  

and  

Finally, if we put c in (4) and (5), we will find a and b:

and  

and

So the vector and

I hope it helps you!

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explanation:

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