Chapter 3: Q79P (page 61)

In Fig. 3-38 , the magnitude of $\overset{⇀}{a} is 4.3$ , the magnitude of $\overset{⇀}{b} is 5.4$ , and $ϕ = 46 °$ . Find the area of the triangle contained between the two vectors and the thin diagonal line.

Short Answer

Expert verified

Area of a triangle is8.4

Step by step solution

To understand the concept

The magnitude of the vector product is the area of parallelogram spanned by these two vectors. Therefore, vector product is used to compute the area of a triangle.

Here the area of a triangle is given by,

$A = \frac{1}{2} |\overset{⇀}{a} \times \overset{⇀}{b}| = \frac{1}{2} ab sinϕ (1) Given, \overset{⇀}{a} = 4.3 \overset{⇀}{b} = 5.4 The angle between the vector \overset{⇀}{a} and \overset{⇀}{b} is ϕ = 46 °$

To find the area of a triangle

Substituting the values of $\overset{⇀}{a}, \overset{⇀}{b}$ , and $ϕ$ in equation (i), the area of a triangle is given by

$A = \frac{1}{2} absinϕ = \frac{1}{2} (4.3) (5.4) \sin (46)$

Thus area of triangle $A = 8.4$

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In Fig. 3-38 , the magnitude of $\overset{⇀}{a} is 4.3$ , the magnitude of $\overset{⇀}{b} is 5.4$ , and $ϕ = 46 °$ . Find the area of the triangle contained between the two vectors and the thin diagonal line.

Short Answer

Step by step solution

To understand the concept

To find the area of a triangle

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In Fig. 3-38 , the magnitude of a⇀is4.3, the magnitude of b⇀is5.4, and ϕ=46°. Find the area of the triangle contained between the two vectors and the thin diagonal line.

Short Answer

Step by step solution

To understand the concept

To find the area of a triangle

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Thermodynamics

Kinematics Physics

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Study anywhere. Anytime. Across all devices.

In Fig. 3-38 , the magnitude of $\overset{⇀}{a} is 4.3$ , the magnitude of $\overset{⇀}{b} is 5.4$ , and $ϕ = 46 °$ . Find the area of the triangle contained between the two vectors and the thin diagonal line.