Which of the following is an accurate statement about vectors?

the magnitude of a vector may be positive even if all of its components are negative.

the magnitude of a vector can be zero even if one of its components is not zero.

if two vectors have unequal magnitudes, it is possible that their vector sum is zero.

rotating a vector about an axis passing through the tip of the vector does not change the vector.

it is possible to add a scalar quantity to a vector.

The magnitude of a vector may be positive even if all of its components are negative.

Explanation:

A vector has both magnitude and direction unlike a scalar which has magnitude only.

A vector can be written in terms of its components:

The magnitude of the vector is given by:

Thus, even if all the components of the vector are negative, the vector can have a positive magnitude.

The magnitude would be non-zero if one of its components is non-zero.

some of two vectors involves summation of magnitudes of of the vector components in the same direction. Two vectors having unequal magnitudes cannot have vector sum zero.

Rotating a vector about an axis passing through the tip of the vector changes the vector as the direction changes.

A scalar quantity cannot be added to a vector as it lacks the direction.

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards