The vector b = 3j + 4k is to be written as the sum of a vector b1 parallel to a = i + j and a vector b2 perpendicular to a. Then b1 is equal to

Engineering

Mathematics

Linear Combination of Vectors

Scalar Product of Two Vectors

Question

The vector b = 3j + 4k is to be written as the sum of a vector b₁ parallel to a = i + j and a vector b₂ perpendicular to a. Then b₁ is equal to

$\frac{3}{2} (i + j)$

$\frac{2}{3} (i + j)$

$\frac{1}{2} (i + j)$

$\frac{1}{3} (i + j)$

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$b 1 || a \Rightarrow b 1 = a(i + j)$
$b 2 = b - b 1 = (3 - a)i - aj + 4k$
Also, b₃ – a = 0
$\Rightarrow$ $(3 - a) - a = 0 \Rightarrow a = \frac{3}{2}$
$b_{1} = \frac{3}{2} (i + j)$