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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
The vector $\vec{B} = 3\vec{i} + 4\vec{k}$ is to be written as the sum of a vector $\vec{B_1}$ parallel to
$\vec{A} = \vec{i} + \vec{j}$ and a vector $\vec{B_2}$ perpendicular to $\vec{A}$.
Then $\vec{B_1}$ is:
Solution
Parallel component formula: $\displaystyle \vec{B_1} = \frac{\vec{B}\cdot \vec{A}}{\vec{A}\cdot \vec{A}} \vec{A}$ Compute:
$\vec{B} = (3,0,4)$
$\vec{A} = (1,1,0)$
$\vec{B}\cdot\vec{A} = 3\cdot 1 + 0\cdot 1 + 4\cdot 0 = 3$
$\vec{A}\cdot\vec{A} = 1^2 + 1^2 = 2$
Thus:
$\vec{B_1} = \dfrac{3}{2}(\vec{i} + \vec{j})$
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