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.
The Only nutrient whose form is available as both anion and cationic form is
The soils of grassland ecosystems, characterized by a thick, dark surface horizon comes under which soil order?
Which clay mineral group is known for its ability to swell and expand when wetted?
Why does a high C: N ratio in added organic matter initially slow down nitrogen availability for plants?
The term “operational holding” refers to
Blue green algae is used for
Which of the following is the progeny of breeder seed and is responsible for producing certified seed?
What chemical process results in the breakdown of silicate minerals by water, leading to the formation of clay minerals and soluble substances?
Regarding the reclamation of saline soils, which of the following statement is/are correct?
Which process of soil formation is described as the removal of silica from upper layers, concentrating sesquioxides in the solum, and operates favorably...
Relevant for Exams:
Hey, Don't leave. If you have any queries regarding any exam let us know here.
