Question
Vectors a, b, and c satisfy a ⋅  ( b × c ) = 0, and
no two of them are zero. Which of the following is necessarily true?Solution
The scalar triple product a • (b × c) = 0 signifies that the volume of the parallelepiped formed by the vectors a, b, and c is zero. A zero volume directly implies that the three vectors lie in the same plane, meaning they are coplanar. Now consider the other options: a ⊥ b is not necessary; vectors can be coplanar without a and b being perpendicular. a ∥ (b × c) would mean a • (b × c) = |a||b × c| ≠0 (unless one of the vectors is zero), so this is also not necessarily true. In fact, a • (b × c) = 0 implies that a is perpendicular to (b × c). b ⊥ c is also not necessary; even if b and c are not perpendicular, the three vectors can still be coplanar.
What is the tone of the passage according to you?
Choose the word which is most nearly the same in meaning to the word ‘perennial’ as used in the passage.
Which of the following is /are the reason/s for development of cracks on the walls of the houses in Ashraya Colony of Tirthahallai?
(A) Due to fr...
Several studies have pointed out that ________________________________.
Why did the other judges possibly revolt against the CJI according to the passage?
Find the word from the given options which has its meaning most opposite to the word WOEFULLY as used in the passage.
Synonym of fosterÂ
What was the outcome of the German Revolution in relation to the German federal constitutional monarchy?
Why weren’t the photo albums destroyed?
Choose the word which is most nearly the same in meaning to the word ‘prerogative’ as used in the passage .
Relevant for Exams:
