Chapter 3: Q53P (page 60)

A vector $\vec{a}$ of magnitude 10units and another vector $\vec{b}$ of magnitude 6.0units differ in directions by $60 °$ . Find (a) the scalar product of the two vectors and (b) the magnitude of the vector product $\vec{a} \times \vec{b}$ .

Short Answer

Expert verified

a) The scalar product of two vectors, $\vec{a} . \vec{b}$ ,is 30 units

b) The magnitude of the vector product $|\vec{a}, \vec{b}|$ is 52 units.

Step by step solution

Given

The magnitude of the vector $\vec{a}$ is 10 units.

The magnitude of the vector $\vec{b}$ is 6.0 units

The angle between $\vec{a}$ and $\vec{b}$ is $θ = 60 °$

Understanding the concept

Use the formula of the scalar product of two vectors and vector product of two vectors.

Formula:

$\vec{a} . \vec{b} = a b \cos θ$ …………..(i)

$|\vec{a} \times \vec{b}| = a b \sin θ$ …………..(ii)

(a) Calculate the scalar product of two vectors

The dot product of vectors $\vec{a}$ and $\vec{b}$ can be calculated using equation (i)

$\vec{a} . \vec{b} = abcosθ = 10 \times 6 \times 0.5 = 30 units$

Therefore, the dot product of vectors $\vec{a}$ and $\vec{b}$ is 30 units.

(b) Calculate the magnitude of vector product a→×b→

Use the equation (ii) to calculate the cross product ofvectors $\vec{a}$ and $\vec{b}$ .

$|\vec{a} \times \vec{b}| = absin 60 = 52 units$

Therefore, the cross product of vectors $\vec{a}$ and $\vec{b}$ is 52 units.

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A vector $\vec{a}$ of magnitude 10units and another vector $\vec{b}$ of magnitude 6.0units differ in directions by $60 °$ . Find (a) the scalar product of the two vectors and (b) the magnitude of the vector product $\vec{a} \times \vec{b}$ .

Short Answer

Step by step solution

Given

Understanding the concept

(a) Calculate the scalar product of two vectors

(b) Calculate the magnitude of vector product a→×b→

One App. One Place for Learning.

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A vectora→ of magnitude 10units and another vectorb→of magnitude 6.0units differ in directions by60°. Find (a) the scalar product of the two vectors and (b) the magnitude of the vector product a→×b→.

Short Answer

Step by step solution

Given

Understanding the concept

(a) Calculate the scalar product of two vectors

(b) Calculate the magnitude of vector product a→×b→

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Solid State Physics

Radiation

Mechanics and Materials

Kinematics Physics

Rotational Dynamics

Magnetism and Electromagnetic Induction

Study anywhere. Anytime. Across all devices.

A vector $\vec{a}$ of magnitude 10units and another vector $\vec{b}$ of magnitude 6.0units differ in directions by $60 °$ . Find (a) the scalar product of the two vectors and (b) the magnitude of the vector product $\vec{a} \times \vec{b}$ .