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Chapter 10: Q. 20 (page 824)

If u, v, and ware three mutually orthogonal vectors in 鈩�3, explain why u脳(v脳w)=0.

Short Answer

Expert verified

u脳(v脳w)=0becauseu脳(v脳w)=(u路w)v鈭�(u路v)wandu, v, and ware three mutually orthogonal vectors.

Step by step solution

01

Step 1. Given Information  

If u, v, and ware three mutually orthogonal vectors in 鈩�3, explain why u脳(v脳w)=0.

02

Step 2. It is given that u, v, and w are three mutually orthogonal vectors in ℝ3.

As we know that u脳(v脳w)=(u路w)v鈭�(u路v)w

Since u, v, and ware three mutually orthogonal so the u路wandu路vis zero.

So

u脳(v脳w)=0脳v鈭�0脳wu脳(v脳w)=0

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Most popular questions from this chapter

If u and v are nonzero vectors in 鈩�3, why do the equations role="math" localid="1649263352081" u路(u脳v)=0 and v路(u脳v)=0 tell us that the cross product is orthogonal to both u and v?

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

v=15,13

If the triple scalar product u路(v脳w) is equal to zero, what geometric relationship do the vectors u, v and w have?

How is the determinant of a 3 脳 3 matrix used in the computation of the determinant of two vectorsu=(u1,u2,u3)andv=(v1,v2,v3)?

In Exercises 30鈥�35 compute the indicated quantities when u=(鈭�3,1,鈭�4),v=(2,0,5),andw=(1,3,13)

role="math" localid="1649434688557" v脳wandw脳v
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