Question:
If a vector 2î+3ĵ+8 is perpendicular to the vector 4ĵ-4î+α,then the value of α is:
If a vector 2î+3ĵ+8 is perpendicular to the vector 4ĵ-4î+α,then the value of α is:
Updated On: Apr 21, 2025
-2
\(\frac{1}{2}\)
\(-(\frac{1}{2})\)
2
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The Correct Option is C
Solution and Explanation
A =2\(\hat{i}\)+3\(\hat j\)+8\(\hat k\)
B =4\(\hat i\)−4\(\hat j\)+a\(\hat k\)
Given that A and B are parallel, A. B = 0 (2\(\hat{i}\)+3\(\hat j\)+8\(\hat k\))(4\(\hat i\)−4\(\hat j\)+a\(\hat k\))
8−12+8a=0
a= \(\frac{4}{8}\) = \(\frac{1}{2}\)
B =4\(\hat i\)−4\(\hat j\)+a\(\hat k\)
Given that A and B are parallel, A. B = 0 (2\(\hat{i}\)+3\(\hat j\)+8\(\hat k\))(4\(\hat i\)−4\(\hat j\)+a\(\hat k\))
8−12+8a=0
a= \(\frac{4}{8}\) = \(\frac{1}{2}\)
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Concepts Used:
Multiplication of a Vector by a Scalar
When a vector is multiplied by a scalar quantity, the magnitude of the vector changes in proportion to the scalar magnitude, but the direction of the vector remains the same.
Properties of Scalar Multiplication:
The Magnitude of Vector:
In contrast, the scalar has only magnitude, and the vectors have both magnitude and direction. To determine the magnitude of a vector, we must first find the length of the vector. The magnitude of a vector formula denoted as 'v', is used to compute the length of a given vector ‘v’. So, in essence, this variable is the distance between the vector's initial point and to the endpoint.