Dtermine the value of a so that
u=2i+aj+k and 4i-2j-2k are perpendicular
Did you just start this topic?
This is a very easy question.
if two vectors are perpendicular, then their dot product must be zero
then (2,a,1).(4,-2,-2)=0
8-2a-2=0
a=3
To determine the value of "a" such that the given vectors are perpendicular, we can use the dot product.
The dot product of two vectors is calculated by multiplying their corresponding components and adding the results.
Given vectors:
u = 2i + aj + k
v = 4i - 2j - 2k
For the vectors to be perpendicular, their dot product must be zero.
To find the dot product, we multiply the corresponding components and sum them:
u Β· v = (2 * 4) + (a * -2) + (1 * -2) = 8 - 2a - 2
Equating this to zero:
8 - 2a - 2 = 0
Simplifying the equation:
6 - 2a = 0
Now solve for "a" by isolating it on one side of the equation:
-2a = -6
a = -6 / -2
a = 3
Hence, the value of "a" that makes the vectors u and v perpendicular is 3.