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#556 Mathematics Vector Algebra
MCQ_SINGLE APPLY 2024 AISSCE(Board Exam)
KNOWLEDGE 1 Marks
If \(\vec{a}=2\hat{i}-\hat{j}+\hat{k}\) and \(\vec{b}=\hat{i}+\hat{j}-\hat{k}\), then \(\vec{a}\) and \(\vec{b}\):
(A) collinear vectors which are not parallel
(B) parallel vectors
(C) perpendicular vectors
(D) unit vectors
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#555 Mathematics Vector Algebra
MCQ_SINGLE APPLY 2024 AISSCE(Board Exam)
KNOWLEDGE 1 Marks
If \(|\vec{a}|= 2\) and \(-3\le k\le2\), then \(|\vec{k}\vec{a}|\in\):
(A) [-6, 4]
(B) [0, 4]
(C) [4, 6]
(D) [0, 6]
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#554 Mathematics Vector Algebra
MCQ_SINGLE APPLY 2024 AISSCE(Board Exam)
KNOWLEDGE 1 Marks
If \(\vec{a}\) and \(\vec{b}\) are two vectors such that \(|\vec{a}|=1,|\vec{b}|=2~and\vec{a}\cdot\vec{b}=\sqrt{3}\) then the angle between \(2\vec{a}\) and \(-\vec{b}\) is:
(A) \(\frac{\pi}{6}\)
(B) \(\frac{\pi}{3}\)
(C) \(\frac{5\pi}{6}\)
(D) \(\frac{11\pi}{6}\)
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#553 Mathematics Vector Algebra
MCQ_SINGLE APPLY 2024 AISSCE(Board Exam)
Competency 1 Marks
The vectors \(\vec{a}=2\hat{i}-\hat{j}+\hat{k}\), \(\vec{b}=\hat{i}-3\hat{j}-5\hat{k}\) and \(\vec{c}=-3\hat{i}+4\hat{j}+4\hat{k}\) represents the sides of
(A) an equilateral triangle
(B) an obtuse-angled triangle
(C) an isosceles triangle
(D) a right-angled triangle
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#552 Mathematics Vector Algebra
MCQ_SINGLE APPLY 2024 AISSCE(Board Exam)
Competency 1 Marks
Let \(\vec{a}\) be any vector such that \(|\vec{a}|=a\) The value of \(|\vec{a}\times\hat{i}|^{2}+|\vec{a}\times\hat{j}|^{2}+|\vec{a}\times\hat{k}|^{2}\) is:
(A) \(a^{2}\)
(B) \(2a^{2}\)
(C) \(3a^{2}\)
(D) 0
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#551 Mathematics Vector Algebra
MCQ_SINGLE APPLY 2024 AISSCE(Board Exam)
Competency 1 Marks
The position vectors of points P and Q are \(\vec{p}\) and \(\vec{q}\) respectively. The point R divides line segment PQ in the ratio 3:1 and S is the mid-point of line segment PR. The position vector of S is:
(A) \(\frac{\vec{p}+3\vec{q}}{4}\)
(B) \(\frac{\vec{p}+3\vec{q}}{8}\)
(C) \(\frac{5\vec{p}+3\vec{q}}{4}\)
(D) \(\frac{5\vec{p}+3\vec{q}}{8}\)
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