Chapter 3: Q21P (page 105)

Show that $B | A | + A | B |$ and $A | B | - B | A |$ are orthogonal.

Short Answer

Expert verified

$B | A | + A | B |$ and $A | B | - B | A |$ are orthogonal.

Step by step solution

Concept and formula used for the given vector

Write the expression for perpendicular vectors.

$P \times Q = 0 . . . . . . . . . . (1)$

Here, $P$ and $Q$ are vectors.

To show that the given vectors are orthogonal

To calculate the dot product of the vectors,

$\Rightarrow P \cdot Q \Rightarrow (B | A | + A | B |) \cdot (A | B | - B | A |) \Rightarrow (A | B |)^{2} - (B | A |)^{2} \Rightarrow (A \cdot A)^{2} (| B |)^{2} - (B \cdot B)^{2} (| A |)^{2} \Rightarrow (| A |)^{2} (| B |)^{2} - (| B |)^{2} (| A |)^{2} \Rightarrow 0$

Therefore, the scalar product of vectors is zero. Thus, the vectors are perpendicular.

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Show that $B | A | + A | B |$ and $A | B | - B | A |$ are orthogonal.

Short Answer

Step by step solution

Concept and formula used for the given vector

To show that the given vectors are orthogonal

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Show that B|A|+A|B|andA|B|-B|A|are orthogonal.

Short Answer

Step by step solution

Concept and formula used for the given vector

To show that the given vectors are orthogonal

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Waves Physics

Wave Optics

Physics of Motion

Magnetism and Electromagnetic Induction

Electric Charge Field and Potential

Thermodynamics

Study anywhere. Anytime. Across all devices.

Show that $B | A | + A | B |$ and $A | B | - B | A |$ are orthogonal.