Which of the following points in space will have position with respect to the or | TestHub

Passage / Comprehension

In an open 3D-space, where an object can move easily in any direction, its position with respect to origin O is given by $r = x \hat{i} + y \hat{j} + z \hat{k}$ , and its distance from the origin is $∣ r ∣ = x^{2} + y^{2} + z^{2}$ .

Using this convention of 3D vectors, consider three points: A (1,1,1), B(2,0,0), and C(3,4,5).

Which of the following points in space will have position with respect to the origin in perpendicular direction to the position of point A with respect to origin.

Options:

Answer:

Solution:

For a perpendicular direction, the dot product must be zero.

So, $(x) (1) + y (1) + z (1) = 0$ or $x + y + z = 0$ .

Option (A): $(1) + (-1) + (-1) \neq = 0$ .

Option (B): $(-1) + (1) + (2) \neq = 0$ .

Option (C): $(2) + (-1) + (-1) = 0$ .

Option (D): $(1) + (1) + (2) \neq = 0$ .

Thus, the correct answer is (C).

Physics - Vectors Question with Solution | TestHub

Options:

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