Use the cross product to find the sine of the angle between the vectors u=\le

CoormaBak9

CoormaBak9

Answered question

2021-09-27

Use the cross product to find the sine of the angle between the vectors u=(2,3,6) and v=(2,3,6).

Answer & Explanation

i1ziZ

i1ziZ

Skilled2021-09-28Added 92 answers

From the given formula we have:
u×v∥=∥u∥∥vsinθ
where θ[0,π]θ[0,π] is the angle between the vectors u and v. This suggests:
sinθ=u×vu∥∥v
In our situation, we have:
u×v=(2,3,6)×(2,3,6)=(|3636|,|2626|,|2323|)=(36,24,0)
u×v∥=∥(36,24,0)∥=362+(24)2+0=1872=1213
u∥=∥(2,3,6)∥=22+32+(6)2=4+9+36=49=7
v∥=∥(2,3,6)∥=22+32+62=4+9+36=49=7
Then sinθ=1213490.8830

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