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Chapter 1: Problem 77
If a vector \(2 \hat{i}+3 \hat{j}+8 \hat{k}\) is perpendicular to the vector \(4 \hat{j}-4 \hat{i}+\alpha \hat{k}\) then the value of \(\alpha\) is (A) \(\frac{1}{2}\) (B) \(\frac{-1}{2}\) (C) 1 (D) \(-1\)
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If \(\vec{B}=\lambda \vec{A}\) then \(\frac{\vec{B}}{\vec{A}}=\ldots\) (A) \(\lambda\) (B) \(\frac{1}{\lambda}\) (C) \(\frac{\lambda}{2}\) (D) Indeterminate
The length, width and thickness of a block are (100.0 \(\pm 0.1) \mathrm{cm},(10.00 \pm 0.01) \mathrm{cm}\) and \((1.000 \pm 0.001) \mathrm{cm}\) respectively. The maximum possible error in its volume will be (A) \(\pm 0.111 \mathrm{~cm}^{3}\) (B) \(\pm 0.012 \mathrm{~cm}^{3}\) (C) \(+0.03 \mathrm{~cm}^{3}\) (D) None of these
\(\vec{a}, \vec{b}, \vec{c}\) are three coplanar vectors. Find the vector sum. \(\vec{a}=4 \hat{i}-\hat{j}, \vec{b}=-3 \hat{i}+2 \hat{j}, \vec{c}=-3 \hat{j}\) (A) \(\sqrt{5}, 297^{\circ}\) (B) \(\sqrt{5}, 63^{\circ}\) (C) \(\sqrt{3}, 297^{\circ}\) (D) \(\sqrt{3}, 63^{\circ}\)
The component of vector \(\vec{A}=2 \hat{i}+3 \hat{j}\) along the vector \(\hat{i}+\hat{j}\) is (A) \(\frac{5}{\sqrt{2}}\) (B) \(10 \sqrt{2}\) (C) \(5 \sqrt{2}\) (D) 5
A force \(6 \hat{i}+3 \hat{j}+\hat{k}\) Newton displaces a particles from \(A(0,3,2)\) to \(B(5,1,6)\). Find the work done. (A) \(10 \mathrm{~J}\) (B) \(22 \mathrm{~J}\) (C) \(32 \mathrm{~J}\) (D) \(\underline{41 J}\)
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