Q36P If d鈬赌1=3i^-2j^+4k^聽and d鈬赌2=... [FREE SOLUTION]

Chapter 3: Q36P (page 59)

If ${\overset{鈬赌}{d}}_{1} = 3 \hat{i} - 2 \hat{j} + 4 \hat{k}$ and ${\overset{鈬赌}{d}}_{2} = - 5 \hat{i} + 2 \hat{j} - \hat{k}$ then what is $({\overset{鈬赌}{d}}_{1} + {\overset{鈬赌}{d}}_{2}) . ({\overset{鈬赌}{d}}_{1} 脳 4 {\overset{鈬赌}{d}}_{2})$ ?

Short Answer

Expert verified

The product, $({\overset{鈬赌}{d}}_{1} + {\overset{鈬赌}{d}}_{2}) . ({\overset{鈬赌}{d}}_{1} 脳 4 {\overset{鈬赌}{d}}_{2})$ is equal to 0.

Step by step solution

Vector operations

The dot product of perpendicular vectors is equal to zero. The cross-product of two vectors results in a vector that is perpendicular to both vectors.

Find the value for $({\overset{鈬赌}{d}}_{1} + {\overset{鈬赌}{d}}_{2})$ and $({\overset{鈬赌}{d}}_{1} 脳 4 {\overset{鈬赌}{d}}_{2})$ separately and then take the dot product of them to find the required answer.

The given vectors are,

$\overset{鈬赌}{d_{1}} = 3 \hat{i} - 2 \hat{j} + 4 \hat{k} {\overset{鈬赌}{d}}_{2} = - 5 \hat{j} + 2 \hat{j} - \hat{k}$

Calculating the cross and dot product

${\overset{鈬赌}{d}}_{1} + {\overset{鈬赌}{d}}_{2}$ will lie in the same plane i.e., in the plane of ${\overset{鈬赌}{d}}_{1} and {\overset{鈬赌}{d}}_{2}$ .

${\overset{鈬赌}{d}}_{1} 脳 4 {\overset{鈬赌}{d}}_{2}$ will lie in the plane which is perpendicular to the plane of ${\overset{鈬赌}{d}}_{1} and {\overset{鈬赌}{d}}_{2}$ .

As they are perpendicular to each other the dot product of ${\overset{鈬赌}{d}}_{1} + {\overset{鈬赌}{d}}_{2}$ and ${\overset{鈬赌}{d}}_{1} 脳 4 {\overset{鈬赌}{d}}_{2}$ will be zero.

role="math" localid="1656309525133" $({\overset{鈬赌}{d}}_{1} + {\overset{鈬赌}{d}}_{2})$ . $({\overset{鈬赌}{d}}_{1} 脳 4 {\overset{鈬赌}{d}}_{2})$ =0

Thus, the dot product of $({\overset{鈬赌}{d}}_{1} + {\overset{鈬赌}{d}}_{2})$ and $({\overset{鈬赌}{d}}_{1} 脳 4 {\overset{鈬赌}{d}}_{2})$ is equal to 0.

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91影视

If ${\overset{鈬赌}{d}}_{1} = 3 \hat{i} - 2 \hat{j} + 4 \hat{k}$ and ${\overset{鈬赌}{d}}_{2} = - 5 \hat{i} + 2 \hat{j} - \hat{k}$ then what is $({\overset{鈬赌}{d}}_{1} + {\overset{鈬赌}{d}}_{2}) . ({\overset{鈬赌}{d}}_{1} 脳 4 {\overset{鈬赌}{d}}_{2})$ ?

Short Answer

Step by step solution

Vector operations

Calculating the cross and dot product

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91影视

If d鈬赌1=3i^-2j^+4k^and d鈬赌2=-5i^+2j^-k^then what is (d鈬赌1+d鈬赌2).(d鈬赌1脳4d鈬赌2)?

Short Answer

Step by step solution

Vector operations

Calculating the cross and dot product

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Geometrical and Physical Optics

Quantum Physics

Torque and Rotational Motion

Mechanics and Materials

Electrostatics

Medical Physics

Study anywhere. Anytime. Across all devices.

If ${\overset{鈬赌}{d}}_{1} = 3 \hat{i} - 2 \hat{j} + 4 \hat{k}$ and ${\overset{鈬赌}{d}}_{2} = - 5 \hat{i} + 2 \hat{j} - \hat{k}$ then what is $({\overset{鈬赌}{d}}_{1} + {\overset{鈬赌}{d}}_{2}) . ({\overset{鈬赌}{d}}_{1} 脳 4 {\overset{鈬赌}{d}}_{2})$ ?