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
Answer / Solution

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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