Question

If a, b, and c are vectors and c is a scalar, then we have the following properties. 1. a × b = ?b × a 2. (ca) × b = c(a × b) = a × (cb) 3. a × (b + c) = a × b + a × c 4. (a + b) × c = a × c + b × c 5. a · (b × c) = (a × b) · c 6. a × (b × c) = (a · c)b ? (a · b)c Prove the property a × b = ?b × a of the theorem above. Let a = ?a1, a2, a3? and b = ?b1, b2, b3?. Then, a × b = = (?1) = ?b × a.

          If a, b, and c are vectors and c is a scalar, then we have the following properties.

1. a × b = ?b × a
2. (ca) × b = c(a × b) = a × (cb)
3. a × (b + c) = a × b + a × c
4. (a + b) × c = a × c + b × c
5. a · (b × c) = (a × b) · c
6. a × (b × c) = (a · c)b ? (a · b)c

Prove the property a × b = ?b × a of the theorem above.

Let a = ?a1, a2, a3? and b = ?b1, b2, b3?. Then,

a × b = 

= (?1)

= ?b × a.

If a, b, and c are vectors and c is a scalar, then we have the following properties.

1. a × b = ?b × a
2. (ca) × b = c(a × b) = a × (cb)
3. a × (b + c) = a × b + a × c
4. (a + b) × c = a × c + b × c
5. a · (b × c) = (a × b) · c
6. a × (b × c) = (a · c)b ? (a · b)c

Prove the property a × b = ?b × a of the theorem above.

Let a = ?a1, a2, a3? and b = ?b1, b2, b3?. Then,

a × b =

= (?1)

= ?b × a.

Added by Dolores M.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Rukhmani Jain

12/10/2021

Step 1

The cross product of two vectors a and b is defined as: a x b = (a2b3 - a3b2, a3b1 - a1b3, a1b2 - a2b1) Similarly, the cross product of b and a is: b x a = (b2a3 - b3a2, b3a1 - b1a3, b1a2 - b2a1) If we compare these two results, we can see that each component Show more…

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If a, b, and c are vectors and c is a scalar, then we have the following properties: 1. a x b = -b x a 2. (c a) x b = c(a x b) = a x (c b) 3. a x (b + c) = a x b + a x c 4. (a + b) x c = a x c + b x c 5. a . (b x c) = (a x b) . c 6. a x (b x c) = (a . c) b - (a . b) c Prove the property a x b = -b x a of the theorem above. Let a = (a1, a2, a3) and b = (b1, b2, b3). Then, a x b = = (-1) = -b x a.