Question 10 (OR 2 nd question)
Find the angle between the vectors:
a = i + j – k and b = i – j + k
Last updated at Oct. 1, 2019 by Teachoo
Question 10 (OR 2 nd question)
Find the angle between the vectors:
a = i + j – k and b = i – j + k
Transcript
Question 10 (OR 2nd question) Find the angle between the vectors: ๐ โ = ๐ ฬ + ๐ ฬ โ ๐ ฬ and ๐ โ = ๐ ฬ โ ๐ ฬ + ๐ ฬ Given ๐ โ = ๐ ฬ + ๐ ฬ โ ๐ ฬ and ๐ โ = ๐ ฬ โ ๐ ฬ + ๐ ฬ We know that ๐ โ . ๐ โ = |๐ โ ||๐ โ | cos ฮธ where ฮธ is the angle between ๐ โ & ๐ โ Now, ๐ โ. ๐ โ = (๐ ฬ + ๐ ฬ โ ๐ ฬ). (๐ ฬ โ ๐ ฬ + ๐ ฬ) = (1๐ ฬ + 1๐ ฬ โ ๐ ฬ). (1๐ ฬ โ 1๐ ฬ + 1๐ ฬ) = 1 ร 1 + 1 ร (โ1) + (-1) ร 1 = 1 โ 1 โ 1 = โ1 Magnitude of ๐ โ = โ(12+12+(โ1)2) |๐ โ |= โ(1+1+1) = โ3 Magnitude of ๐ โ = โ(12+(โ1)2+12) |๐ โ |= โ(1+1+1) = โ3 Now, ๐ โ . ๐ โ = |๐ โ ||๐ โ | cos ฮธ โ1 = โ3 ร โ3 ร cos ฮธ โ1 = 3 cos ฮธ cos ฮธ = (โ1)/3 ฮธ = ๐๐๐^(โ๐) ((โ๐)/๐) Thus, the angle between ๐ โ and ๐ โ is cos-1((โ๐)/๐)
CBSE Class 12 Sample Paper for 2019 Boards
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CBSE Class 12 Sample Paper for 2019 Boards
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