If and
Are nonzero vectors for which
•
= 0,it must follow that
A) × = 0.
B) is parallel to .
C) | × | = AB.
D) | × | = 1.

Question

If  and 
Are nonzero vectors for which 
• 
= 0,it must follow that
A) × = 0. 
B) is parallel to . 
C) | × | = AB. 
D) | × | = 1.

Quizplus · Accepted Answer

Using the given vectors, we can expand the equation to get:
(11ea8401_fc25_063a_aeff_810239a0b736_TB6682_00 × 11ea8401_fc25_2d4b_aeff_0583c057a9c5_TB6682_11) = 0
Expanding the cross product, we get:
(11ea8401_fc25_063a_aeff_810239a0b736_TB6682_00 × 11ea8401_fc25_2d4b_aeff_0583c057a9c5_TB6682_11) = 
(11ea8401_fc25_063a_aeff_810239a0b736_TB6682_00 × 11ea8401_fc25_2d4b_aeff_0583c057a9c5_TB6682_11) + 
(11ea8401_fc25_063a_aeff_810239a0b736_TB6682_00 × 11ea8401_fc25_0638_aeff_c1a38b07ccd2_TB6682_11) - 
(11ea8401_fc25_063a_aeff_810239a0b736_TB6682_00 × 11ea8401_fc25_0639_aeff_4305b2c548c0_TB6682_00)
Since the first term is 0 and the second and third terms are equal, we get:
(11ea8401_fc25_063a_aeff_810239a0b736_TB6682_00 × 11ea8401_fc25_2d4b_aeff_0583c057a9c5_TB6682_11) = 
2(11ea8401_fc25_063a_aeff_810239a0b736_TB6682_00 × 11ea8401_fc25_0638_aeff_c1a38b07ccd2_TB6682_11)

Let the left side be denoted by C and the right side by AB.

Taking the magnitude of both sides, we get:
|C| = 2|AB|

Therefore, choice C is true.