Question:
If ABCD is a rectangle, $ AB = 5i + 4j - 3k $ and $ AD = 3i + 2j - k $, then find $ BD $.
If ABCD is a rectangle, $ AB = 5i + 4j - 3k $ and $ AD = 3i + 2j - k $, then find $ BD $.
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To find the vector between two points in a rectangular coordinate system, simply add the component vectors of the two sides.
Updated On: Apr 28, 2025
- \( 6i + 6j - 4k \)
- \( 5i + 6j - 4k \)
- \( 8i + 6j - 4k \)
- \( 6i + 5j - 4k \)
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The Correct Option is A
Solution and Explanation
Given that \( AB = 5i + 4j - 3k \) and \( AD = 3i + 2j - k \), we want to find \( BD \).
We know that:
\[
BD = AB + AD
\]
Substituting the values of \( AB \) and \( AD \):
\[
BD = (5i + 4j - 3k) + (3i + 2j - k)
\]
Now, adding the components:
\[
BD = (5i + 3i) + (4j + 2j) + (-3k - k)
\]
\[
BD = 8i + 6j - 4k
\]
Thus, the correct answer is \( 8i + 6j - 4k \).
Thus, the correct answer is \( 8i + 6j - 4k \).
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