Question

A vector has a direction pointing into the first quadrant (both with components 6.3 +3 x and y components are positive). Find

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Answer #1

We have

C = (6.3i+3)

Let us assume the perpendicular vector is given by

Ā = (.zi+yi)

We know that the dot product of two perpendicular vectors is zero. i.e

AC = 0

(ci+yj).(6.31 + 3) = 0

6.3.r + 3y = 0

The solution is a family of values for x and y. But we are interested only in unit vector for negative x component so, we can take any of the results. So, for x = -1,

6.3 x(-1) + 3y = 0

y= 6.3/3 = 2.1

So, one of the perpendicular vectors is

\vec A=(-1\hat i+2.1\hat j)

And the unit vector in the direction of vector A is

Ā (-1i+2.13) VT-1)2 + (2.12 = 1541(-li +2.1į)

The x component of this unit vector is

A, - ਜ x (2)= -0.13

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