Class 12 Maths MCQ – Product of Two Vectors-2

This set of Class 12 Maths Chapter 10 Multiple Choice Questions & Answers (MCQs) focuses on “Product of Two Vectors-2”.

1. Evaluate the product \((2\vec{a}+5\vec{b}).(4\vec{a}-5\vec{b})\).
a) \(|\vec{a}|^2+2\vec{a}.\vec{b}-15|\vec{b}|^2\)
b) \(8|\vec{a}|^2+2\vec{a}.\vec{b}-15|\vec{b}|^2\)
c) \(8|\vec{a}|^2-4\vec{a}.\vec{b}-15|\vec{b}|^2\)
d) \(|\vec{a}|^2+\vec{a}.\vec{b}-5|\vec{b}|^2\)
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2. Find the magnitude of \(\vec{a}\) and \(\vec{b}\) which are having the same magnitude and such that the angle between them is 60° and their scalar product is \(\frac{1}{4}\).
a) \(|\vec{a}|=|\vec{b}|=\frac{1}{2√2}\)
b) \(|\vec{a}|=|\vec{b}|=\frac{1}{√2}\)
c) \(|\vec{a}|=|\vec{b}|=\frac{1}{2√3}\)
d) \(|\vec{a}|=|\vec{b}|=\frac{2}{√3}\)
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3. If \(\vec{a}=\hat{i}-\hat{j}+3\hat{k}, \,\vec{b}=5\hat{i}-2\hat{j}+\hat{k} \,and \,\vec{c}=\hat{i}-\hat{j}\) are such that \(\vec{a}+μ\vec{b}\) is perpendicular to \(\vec{c}\), then the value of μ.
a) \(\frac{7}{2}\)
b) –\(\frac{7}{2}\)
c) –\(\frac{3}{2}\)
d) \(\frac{7}{9}\)
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4. Find the angle between \(\vec{a} \,and \,\vec{b}\) if \(|\vec{a}|=2,|\vec{b}|=\frac{1}{2√3}\) and \(\vec{a}×\vec{b}=\frac{1}{2}\).
a) \(\frac{2π}{3}\)
b) \(\frac{4π}{5}\)
c) \(\frac{π}{3}\)
d) \(\frac{π}{2}\)
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5. Find the vector product of the vectors \(\vec{a}=2\hat{i}+4\hat{j}\) and \(\vec{b}=3\hat{i}-\hat{j}+2\hat{k}\).
a) \(\hat{i}-19\hat{j}-4\hat{k}\)
b) \(3\hat{i}+19\hat{j}-14\hat{k}\)
c) \(3\hat{i}-19\hat{j}-14\hat{k}\)
d) \(3\hat{i}+5\hat{j}+4\hat{k}\)
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6. If \(\vec{a} \,and \,\vec{b}\) are two non-zero vectors then \((\vec{a}-\vec{b})×(\vec{a}+\vec{b})\)=_________
a) \(2(\vec{a}×\vec{b})\)
b) \((\vec{a}×\vec{b})\)
c) –\(4(\vec{a}×\vec{b})\)
d) \(3(\vec{a}×\vec{b})\)
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7. Find the product \((\vec{a}+\vec{b}).(7\vec{a}-6\vec{b})\).
a) \(2|\vec{a}|^2+6\vec{a}.\vec{b}-3|\vec{b}|^2\)
b) \(8|\vec{a}|^2+5\vec{a}.\vec{b}-5|\vec{b}|^2\)
c) \(2|\vec{a}|^2+6\vec{a}.\vec{b}-8|\vec{b}|^2\)
d) \(7|\vec{a}|^2+\vec{a}.\vec{b}-6|\vec{b}|^2\)
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8. Find the vector product of the vectors \(\vec{a}=-\hat{j}+\hat{k}\) and \(\vec{b}=-\hat{i}-\hat{j}-\hat{k}\).
a) \(2\hat{i}-\hat{j}+\hat{k}\)
b) \(2\hat{i}-\hat{j}-4\hat{k}\)
c) \(\hat{i}+\hat{j}-\hat{k}\)
d) \(2\hat{i}-\hat{j}-\hat{k}\)
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9. If \(\vec{a}=2\hat{i}+3\hat{j}+4\hat{k}\) and \(\vec{b}=4\hat{i}-2\hat{j}+3\hat{k}\). Find \(|\vec{a}×\vec{b}|\).
a) \(\sqrt{685}\)
b) \(\sqrt{645}\)
c) \(\sqrt{679}\)
d) \(\sqrt{689}\)
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10. Find the angle between the vectors if \(|\vec{a}|=|\vec{b}|=3\sqrt{2}\) and \(\vec{a}.\vec{b}=9\sqrt{3}\).
a) \(\frac{π}{6}\)
b) \(\frac{π}{5}\)
c) \(\frac{π}{3}\)
d) \(\frac{π}{2}\)
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Sanfoundry Global Education & Learning Series – Mathematics – Class 12.

To practice all chapters and topics of class 12 Mathematics, here is complete set of 1000+ Multiple Choice Questions and Answers.

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