If The vector A=2i + 3j + aK is perpendicular to B = 5i +3j - 2k, then what is the value of a
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To know the vectors that are perpendicular or orthogonal to each other, the following must be taken into consideration:
1. The scalar or dot product between the two considered vectors must be zero.
2. The angle between the two considered vectors must be zero.
The dot product of two vectors A and B is given by the formula
A.B = ABCosΘ
Since vectors are orthogonal, so Θ=90°
Hence, A.B = ABCos90°
A.B = AB(0)
A.B = 0
Now put the given values, we get:
A.B = (2i+3j+ak) . (5i+3j-2k) =0
(2*5) + (3*3) + [ (a) (-2) ] =0
10+9-2a = 0
19-2a =0
19 = 2a
a = 19/2
This is the required answer.
1. The scalar or dot product between the two considered vectors must be zero.
2. The angle between the two considered vectors must be zero.
The dot product of two vectors A and B is given by the formula
A.B = ABCosΘ
Since vectors are orthogonal, so Θ=90°
Hence, A.B = ABCos90°
A.B = AB(0)
A.B = 0
Now put the given values, we get:
A.B = (2i+3j+ak) . (5i+3j-2k) =0
(2*5) + (3*3) + [ (a) (-2) ] =0
10+9-2a = 0
19-2a =0
19 = 2a
a = 19/2
This is the required answer.
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