Question

If a cross b equal to c cross b and a cross equal to b ka then show that a minus b is parallel to b minus c where is not equal tu d and b is not equal to c

Answer 1

Answer:

a - d is parallel to b - c as their vector product is zero

Explanation:

As we know that

$\vec a \times \vec b = \vec c \times \vec d$

$\vec a \times \vec c = \vec b \times \vec d$

now we will subtract the two given equations

now from first equation we have

$\vec a \times \vec b - \vec c \times \vec d = 0$

$\vec a \times \vec b + \vec d \times \vec c = 0$

Similarly from 2nd equation we have

$\vec a \times \vec c - \vec b \times \vec d = 0$

$\vec a \times \vec c + \vec d \times \vec b = 0$

Now subtract above two equations

$\vec a \times (\vec b - \vec c) + \vec d \times (\vec c - \vec b) = 0$

$\vec a \times (\vec b - \vec c) - \vec d \times (\vec b - \vec c) = 0$

so we have

$(\vec a - \vec d) \times (\vec b - \vec c) = 0$

so we can say

a - d is parallel to b - c as their vector product is zero

#Learn

Topic : Vector Product

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