Question
Let vectors a, b, and c be such thata · b = 0, b · c
= 0, and c · a = 0. If |a| = 2, |b| = 3, |c| = 6, then the volume of the parallelepiped formed is:Solution
We are given that:
- a · b = 0 → vectors a and b are perpendicular
- b · c = 0 → vectors b and c are perpendicular
- c · a = 0 → vectors c and a are perpendicular
Hence, they form a rectangular parallelepiped (i.e., a cuboid), and the volume is given by: Volume = |a · (b × c)| But when vectors are mutually perpendicular, the volume simplifies to: Volume = |a| × |b| × |c| Now substitute: |a| = 2
|b| = 3
|c| = 6 So, Volume = 2 × 3 × 6 = 36
More Quant Miscellaneous Questions
What approximate value will come in place of the question mark (?) in the following question? (Note: You are not expected to calculate the exact value.)...
22.11 × 4.98 + 23.03 × 5.12 – 32.95 + 96.9 × 5.02 =?
- 44.83% of 799.88 + (84.12 X 14.98 ÷ 62.87) = ?² + 55.65
(29.97%) of 9840 + ? + (45.17% of 1240) = (31.99% of 11750)
What approximate value will come in place of the question mark (?) in the following question? (Note: You are not expected to calculate the exact value.)...
? 2 – 17.89 2 + 15.33% of 1199.76 = 49.54% of 49.68
(39.98% of 854.79 – 35.13% of 420.28) ÷ 13.12 × 135.34 = 400.31 + ?
? * 9.34 = (275.09 ÷ 8.89) % of 5125 - 1150.88
96.03% of √225.02 × 14.98 = ? + 19.98
- What approximate value will come in place of the question mark (?) in the following question? (Note: You are not expected to calculate the exact value.)
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