Question:medium

If \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{c}\) are non-collinear vectors such that for some scalars \(x, y, z\), \(x\mathbf{a} + y\mathbf{b} + z\mathbf{c} = \mathbf{0}\), then

Show Hint

Three non-coplanar vectors are linearly independent.
Updated On: Apr 7, 2026
  • \(x = 0, y = 0, z = 0\)
  • \(x \neq 0, y \neq 0, z = 0\)
  • \(x = 0, y \neq 0, z \neq 0\)
  • \(x \neq 0, y \neq 0, z \neq 0\)
Show Solution

The Correct Option is A

Solution and Explanation

Was this answer helpful?
0

Top Questions on 3D Geometry

Questions Asked in MET exam

Helicopters are very different from airplanes. They can do three things that airplanes cannot do. First, when airplanes move upward, they must also move forward, but helicopters can move straight up without moving ahead. Second, helicopters can fly backward, which airplanes cannot do. Third, helicopters can use their rotors to hover in the air, which is impossible for airplanes. Helicopters can perform actions that airplanes cannot, they are used for different tasks. Since, helicopters can take off without moving forward, they do not need a runway for take off. They are used in congested areas where there is no room for airplanes or in isolated areas, which do not have airports. Because they can hover, they are used on firefighting missions to drop water on fires. They are used in logging operations to lift trees out of forests. Helicopters are used as air ambulances to airlift patients out of situations, which are difficult to reach by conventional ambulances. The police used helicopters to follow suspects on the ground or to search for cars on the ground. Of course, helicopters have military uses because of their design and capabilities. 

View Solution