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TG EAMCET (EAPCET) Mathematic Multiple Choice Questions (MCQs)

TG EAMCET - Vector Algebra Questions

TG EAMCET - Vector Algebra Questions (151 to 160)

151. If \( \vec{A} = (2, -3, 4) \) and \( \vec{B} = (1, 2, -1) \), what is the sum of \( \vec{A} + \vec{B} \)?

a) \( (3, -1, 3) \)
b) \( (3, -5, 5) \)
c) \( (2, -1, 4) \)
d) \( (1, -1, 3) \)

Answer: a) \( (3, -1, 3) \)

152. The vector \( \vec{A} = 4\hat{i} - 3\hat{j} + 2\hat{k} \) is multiplied by the scalar 3. What is the result?

a) \( 12\hat{i} - 9\hat{j} + 6\hat{k} \)
b) \( 4\hat{i} - 3\hat{j} + 6\hat{k} \)
c) \( 4\hat{i} - 3\hat{j} - 6\hat{k} \)
d) \( 12\hat{i} - 9\hat{j} - 6\hat{k} \)

Answer: a) \( 12\hat{i} - 9\hat{j} + 6\hat{k} \)

153. The angle between the two vectors \( \vec{A} = 3\hat{i} + 2\hat{j} \) and \( \vec{B} = 4\hat{i} - \hat{j} \) is given by:

a) \( \cos^{-1}\left( \frac{10}{\sqrt{13} \cdot \sqrt{17}} \right) \)
b) \( \cos^{-1}\left( \frac{5}{\sqrt{13} \cdot \sqrt{17}} \right) \)
c) \( \cos^{-1}\left( \frac{8}{\sqrt{13} \cdot \sqrt{17}} \right) \)
d) \( \cos^{-1}\left( \frac{6}{\sqrt{13} \cdot \sqrt{17}} \right) \)

Answer: a) \( \cos^{-1}\left( \frac{10}{\sqrt{13} \cdot \sqrt{17}} \right) \)

154. The linear combination of vectors \( \vec{A} \) and \( \vec{B} \) is given by \( C\vec{A} + D\vec{B} \), where \( C \) and \( D \) are scalars. What does this represent?

a) The dot product of \( \vec{A} \) and \( \vec{B} \)
b) A vector parallel to both \( \vec{A} \) and \( \vec{B} \)
c) A new vector that can be obtained by scaling \( \vec{A} \) and \( \vec{B} \)
d) The cross product of \( \vec{A} \) and \( \vec{B} \)

Answer: c) A new vector that can be obtained by scaling \( \vec{A} \) and \( \vec{B} \)

155. If \( \vec{A} = 3\hat{i} - 4\hat{j} + 5\hat{k} \) and \( \vec{B} = 6\hat{i} + 8\hat{j} - 10\hat{k} \), what is the scalar product \( \vec{A} \cdot \vec{B} \)?

a) 3
b) 0
c) 40
d) 45

Answer: c) 40

156. What is the vector equation of a line passing through the point \( (1, 2, 3) \) in the direction of vector \( \vec{d} = (4, -1, 2) \)?

a) \( \vec{r} = (1, 2, 3) + t(4, -1, 2) \)
b) \( \vec{r} = (1, 2, 3) + t(2, 1, 4) \)
c) \( \vec{r} = (0, 0, 0) + t(4, -1, 2) \)
d) \( \vec{r} = (1, 2, 3) + t(-4, 1, -2) \)

Answer: a) \( \vec{r} = (1, 2, 3) + t(4, -1, 2) \)

157. The components of a vector \( \vec{A} = 2\hat{i} + 3\hat{j} + 4\hat{k} \) in three dimensions are:

a) \( (2, 3, 4) \)
b) \( (3, 2, 4) \)
c) \( (4, 2, 3) \)
d) \( (2, 4, 3) \)

Answer: a) \( (2, 3, 4) \)

158. What is the Cartesian equivalent of the vector equation \( \vec{r} = (1, 2, 3) + t(4, -1, 2) \)?

a) \( x = 1 + 4t, y = 2 - t, z = 3 + 2t \)
b) \( x = 1 + 4t, y = 2 + t, z = 3 - 2t \)
c) \( x = 1 + 2t, y = 2 - t, z = 3 + t \)
d) \( x = 1 - 4t, y = 2 + t, z = 3 - 2t \)

Answer: a) \( x = 1 + 4t, y = 2 - t, z = 3 + 2t \)

159. If two vectors \( \vec{A} = (a, b, c) \) and \( \vec{B} = (x, y, z) \) are parallel, then which of the following is true?

a) \( \frac{a}{x} = \frac{b}{y} = \frac{c}{z} \)
b) \( \vec{A} \times \vec{B} = 0 \)
c) \( \vec{A} \cdot \vec{B} = 0 \)
d) Both a and b

Answer: d) Both a and b

160. The components of the vector \( \vec{A} = 3\hat{i} - 2\hat{j} + \hat{k} \) in the \( x \), \( y \), and \( z \) directions are:

a) \( (3, -2, 1) \)
b) \( (2, 3, 1) \)
c) \( (1, -2, 3) \)
d) \( (1, 2, 3) \)

Answer: a) \( (3, -2, 1) \)

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