Generate Quiz 6A24792FEA6C3

When all of the forces acting on a body add up to zero, the body is said to be in equilibrium. When an object’s total acceleration is zero, it indicates that it is in translational equilibrium. As a result, it is either stationary or traveling at a steady speed.

Given:

7i^ + 7k^ = A + B

A – B = -i^ + k^

We must remove B from these equations in order to determine the magnitude of A. By combining the two equations, we can accomplish this:

(7i^ + 7k^) + (-i^ + k^) = (A + B) + (A – B)

Separately simplifying the left and right sides:

2A = 6i^ + 8k^

Both sides are divided by two:

A = 3i^ + 4k^

The vector A is now available. We can utilize the following formula to determine its magnitude:

√(Ax² + Ay² + Az²) = |A|

Ax = 3, Ay = 0, and Az = 4 in this instance. Changing these numbers in the formula:

√(3² + 0² + 4²) = |A|

= √(9 + 0 + 16)

= -25

= 5.

Consequently, A’s magnitude is 5. Option C is therefore the right response.

Think of A and B as having a ∅ angle.

The vector A + B’s resultant is as follows:

√(A²+B²+2AB cos∅) = R

The A-B vector’s resultant is provided as

(A²+B²-2AB cos∅) = R

As stated in the question,

|A+B| = |A-B|

√A² + B² + 2AB cos∅ = √(A² + B²-2AB cos∅)

Resolving,

4ABcos∅ = 0

Cos ∅ = 0.

∅ = 90°

Displacement is a vector quantity, which explains this. A vector quantity possesses both direction and magnitude.

Work done is equal to F x d, as we know.

where d is the displacement in the force’s direction and F is the force.

A constant force, F = 2i + 3j + 4k, is applied, according to the question statement. The force component in the z-direction, or the body’s displacement direction, is equal to 4N.

Thus, work completed equals 4 x 5.

20 J is the equivalent.

=(3)(2)+(-2)(2)+(4)(-3)

=6-4-12

=-10

We determine the angle by using

x component/y component = tan

Thus, tan = √3/1, and we determine the angle by inversely tan.

Consequently, the angle is equal to tan-1 (1/√3)

= 30 degrees.

Since it is numerical, there is only one possible response.

Kinetic energy is a scalar quantity, while force is a vector quantity.

Since displacement, acceleration, and velocity all have magnitude and direction associated with them, they are vector quantities.

Since the scalar product of perpendicular vectors is always zero by rule, the scalar product of k and i+j is also zero.

Therefore, option A is the right response.

Theoretically, every other choice is wrong.