Suppose A=3i-2j+k, B=-i-4j+3k&C is a vector lying along x-axis with the property that A.(B+C)=0. Then find vector C.
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Student
Student
To find the vector C, we need to use the given property A.(B+C) = 0.
First, let's calculate A.B. The dot product of two vectors A and B is given by:
A.B = (3i - 2j + k) . (-i - 4j + 3k)
= 3*(-1) + (-2)*(-4) + 1*3
= -3 + 8 + 3
= 8
Now, let's rewrite the property A.(B+C) = 0 by substituting B and C in terms of their components:
A.(B+C) = 0
(3i - 2j + k) . (Cx i)
= (3*C) + (-2*0) + (1*0)
= 3C
Now we have the equation 3C = 0. To satisfy this equation, C must be equal to zero:
C = 0
Therefore, the vector C is the zero vector, or C = 0.
Note: The zero vector is a special vector that has a length of zero and no specific direction.