Let a = 2i - 3j + 4k and b = 7i + j - 6k. If r × a = r × b, r ⋅ (i + 2j + k) = -3, then r ⋅ (2i - 3j + k) is equal to:
Let a = 2i - 3j + 4k and b = 7i + j - 6k. If r × a = r × b, r ⋅ (i + 2j + k) = -3, then r ⋅ (2i - 3j + k) is equal to:
Option 1 -
10
Option 2 -
12
Option 3 -
8
Option 4 -
13
-
1 Answer
-
Correct Option - 2
Detailed Solution:Given r × a = r × b, which means r × a - r × b = 0 ⇒ r × (a - b) = 0.
This implies that vector r is parallel to vector (a - b).
So, r = λ (a - b) for some scalar λ.
a - b = (2i - 3j + 4k) - (7i + j - 6k) = -5i - 4j + 10k.
So, r = λ (-5i - 4j + 10k).
We are also given r ⋅ (i + 2j + k) = -3.
λ (-5i - 4j + 10k) ⋅ (i + 2j + k) = -3
λ (-51 - 42 + 10*1) = -3
λ (-5 - 8 + 10) = -3
λ (-3) = -3 ⇒ λ = 1.
So, r = 1 * (-5i - 4j + 10k) = -5i - 4j + 10k.
We need to find r ⋅ (2i - 3j + k).
(-5i - 4j + 10k) ⋅ (2i - 3j + k) = (-5) (2) + (-4) (-3) + (...more
Similar Questions for you
|3a+4b|² = 9|a|² + 16|b|² + 24a·b
But a·b = 0, |a|=|b|=k
|3a+4b| = 5k
|4a-3b|
10k = 20? k = 2 = |a| = |b|
Taking an Exam? Selecting a College?
Get authentic answers from experts, students and alumni that you won't find anywhere else
Sign Up on ShikshaOn Shiksha, get access to
- 65k Colleges
- 1.2k Exams
- 682k Reviews
- 1800k Answers