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Question : 36 of 60
Marks:
+1,
-0
Solution:
To find the value of
|×|, remember that the relationship with the dot product and magnitudes is given by:
|×|=||||sin‌θwhere
θ is the angle between the vectors
and
.
We use the formula for the dot product to calculate
cos‌θ :
⋅=||||cos‌θGiven:
‌||=10‌||=2‌⋅=12 Substitute these values into the dot product formula:
12=10×2×cos‌θThus,
12=20‌cos‌θ⟹cos‌θ=‌=‌Since
sin‌2θ+cos2θ=1, we find
sin‌θ :
‌sin‌2θ=1−(‌)2=1−‌=‌‌sin‌θ=‌Now, substitute back to find the magnitude of the cross product:
|×|=10×2×‌=20×‌=16Therefore, the value of
×∣ is 16 .
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