Therefore, the value of the scalar k for which the two vectors are orthogonal is k =1/5.
In physics and mathematics, the term "vector" is used to refer, informally, to certain quantities that cannot be described by a single number or to certain constituents of vector spaces.
Here,
When the dot product of two vectors is zero, those two vectors are said to be orthogonal.
Dot product:
Let's assume we have the two vectors a and b.
a = (1,2) (1,2)
b = (2,3) (2,3)
Their dot item is:
a.b = (1,2). (1,2).
(2,3) = 1*2 + 2*3 = 8
Regarding this issue:
u = (2,3) (2,3)
(k + 1, k - 1) = v
So
u.v = (2,3). (2,3).
(k + 1, k - 1) = 2k + 1, 3k - 1, or 2k + 2, 3k - 3, or 5k - 1
The vectors must be orthogonal for the dot product to equal 0.
So:
=> 5k -1 =0
=> 5k =1
=> k =1/5
Therefore , the value of the scalar k for which the two vectors are orthogonal is k =1/5.
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