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.
Which protocol is used to transfer files over the internet?
Which among the following is internet Standard Protocol?
Which out of following is not a file extension of a video file?
Harmful programs used to disrupt computer operation, gather sensitive information, or gain access to private computer systems are commonly referred to as:
Who is recognised as the Father's of the Internet?
To undo the last work, we have to use which of the following Windows shortcut key?
South Bridge is ________
The operating system that is self-contained in a device and resident in the ROM is ______
A permanent electronic portable storage device that plugs into a USB port is called a _________.
Which of the following is a Web browser?
Relevant for Exams:
