If the vectors À=i+j+3k and B = xî - 2j-k are perpendicular to each other then the positive value of 'x' is
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Answers
Answered by
2
Answer:
If the two vectors are perpendicular to each other, then their dot product is zero.
A. B= AB cosФ = AB cos 90 ( cos 90 = 0 )
therefore, AB = 0
⇒ (1 × x) + ( 1 × -2 ) + ( 3 × -1)= 0
⇒ x - 2 - 3 = 0
⇒ x= 5
Answered by
33
Answer:
x = 5
Concept used:
If 2 vectors are said to be perpendicular, then their dot product will be equal to zero.
Solution:
A . B = 0
→ (1i + 1j + 3k) . (xi - 2j - k) = 0
Take products of their respective vectors.
→ 1(x) + 1(-2) + 3(-1) = 0
⇒ x - 2 - 3 = 0
⇒ x - 5 = 0
⇒ x = 5
∴ The value of x is 5.
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