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Chapter 10: Q.33 (page 849)

Find a unit vector orthogonal to both \(u=<2,4,-1>\) and \(v=<0,-3,2>\).

Short Answer

Expert verified

The unit vector is \(\frac{5}{\sqrt{77}}i-\frac{4}{\sqrt{77}}j-\frac{6}{\sqrt{77}}k \).

Step by step solution

01

Given Information

The given vectors are \(u=<2,4,-1>\) and \(v=<0,-3,2>\).

The orthogonal vector is \(\vec{b}=5i-4j-6k\).

The unit vector \(\hat{b}=\frac{\vec{b}}{|b|}\).

02

Find the unit vector

\(\begin{align*}\hat{b}&=\frac{5i-4j-6k}{\sqrt{5^2+(-4)^2+(-6)^2}}\\&=\frac{5}{\sqrt{77}}i-\frac{4}{\sqrt{77}}j-\frac{6}{\sqrt{77}}k\end{align*}\)

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Most popular questions from this chapter

In Exercises 37鈥�42, find v and find the unit vector in the direction of v.

v=13,-23

In Exercises 36鈥�41 use the given sets of points to find:

(a) A nonzero vector N perpendicular to the plane determined by the points.

(b) Two unit vectors perpendicular to the plane determined by the points.

(c) The area of the triangle determined by the points.

P(1,4,6),Q(鈭�3,5,0),R(3,2,鈭�1)

If u, v and w are three vectors in 鈩�3, what is wrong with the expression u脳v脳w?

Calculate each of the limits:

limh鈫�011+h-1h.

In Exercises 36鈥�41 use the given sets of points to find:

(a) A nonzero vector N perpendicular to the plane determined by the points.

(b) Two unit vectors perpendicular to the plane determined by the points.

(c) The area of the triangle determined by the points.

P(2,鈭�5,1),Q(鈭�4,5,8),R(鈭�1,鈭�5,3)
See all solutions

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