Generate Quiz 68DAC08B635FE

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°

A quantity must adhere to the vector addition rules in order to be considered a vector since they make it possible to combine magnitudes and directions in a methodical manner. These rules include the inverse element of addition, identity element for addition, commutative property of addition, and associative property of addition. Therefore, a vector can be defined as a quantity that complies with vector addition rules. Therefore, choice C is the right response.

Meters are the unit of measurement for displacement. Option A is therefore accurate.

The clockwise and anticlockwise moments of the rod must coincide for it to be balanced.

5×50 = 10×x

x = 25 cm 50 + 25 = 75 cm.

250/10 = x

There is only one possible response because it is a numerical question.

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

To determine vector E’s projection onto the direction of

vector F, the following formula can be applied:

E’s projection onto F is equal to (E dot F) / |F|

Let’s first determine the dot product of E and F: E dot F =

(2)(1) + (-3)(2) + (6)(2) = 2 – 6 + 12 = 8

The magnitude of vector F must then be determined: |F| = √(1² + 2² + 2²) = √9 = 3

We can now compute the forecast: E’s projection onto F

= (E dot F) / |F| = 8 / 3 ≈ 2.67

Consequently, the vector E projection onto the direction of

The vector F is roughly 2.67.

The velocity of an object at a particular moment in time is known as its instantaneous velocity. It is the rate at which the displacement of the object changes in relation to time at that specific moment. Stated differently, it is the slope of the position-time graph of the object at a specific moment in time.

The derivative of an object’s displacement (s) with respect to time (t) can be used to mathematically express the object’s instantaneous velocity (v) at time t:

v(t) = ∆s/∆t

where:

Instantaneous velocity at time t is equal to v(t).

∆s is the infinitesimally small change in displacement (distance traveled) over an infinitely brief period of time.

dt is the infinitesimally small change in time over that same infinitesimally brief period of time.