GATE (TF) Textile 2017 Question Paper Solution | GATE/2017/TF/01

Question 01 (Textile Engineering & Fibre Science)

If the scalar projection of the vector $\vec{a}=3\hat{i}+\beta\hat{k}$ on the vector $\vec{b}=2\hat{i}-2\hat{j}+\hat{k}$ is 5. then a value of $\beta$ is equal to

(A)	21
(B)	9
(C)	-1
(D)	-6

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Scalar projection of the vector $\vec{a}=3\hat{i}+\beta\hat{k}$ on the vector $\vec{b}=2\hat{i}-2\hat{j}+\hat{k}$ is 5
$\beta$ =?
i.e. $\vec{a} \cdot \vec{b}=5$
$\frac{6-0-\beta}{\sqrt(4+4+1)}=5$
$\frac{6-0-\beta}{\sqrt(9)}=5$
$\frac{6-0-\beta}{3}=5$
$(6-\beta)=15$
$\beta=-9$
$\beta=9$ (Ans)

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