If A = i + 2j + 3k and B = 3i - 2j + k, then the area of parallelogram formed from these vectors as the adjacent sides will be
(A) 2√3 square units
(B) 4√3 square units
(C) 6√3 square units
(D) 8√3 square units
1 Answers
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The area of a parallelogram formed by the lines `a x+-b x+-c=0` is `(c^2)/((a b))` (b) `(s c^2)/((a b))` `(c^2)/(2a b)` (d) none of these
Correct Answer - B The given lines are `ax+-by+-c=0` `"or " (x)/(+-c//a) +(y)/(+-c//b)=1` The vertices of rhombus are at A(c/a,0), C(-c/a,0), B(0,c/b), D(0,-c/b). Therefore, the diagonals AC and BD of quadrilateral...
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If the area of the triangle formed by the points `(2a ,b)(a+b ,2b+a),` and `(2b ,2a)` is `2qdotu n i t s ,` then the area of the triangle whose vertic
Correct Answer - 8 We know that the area of the triangle formed by joining the midpoints of any triangle is one-fourth of that triangle. Therefore, Required area `=8`
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If two sides of a triangle are roots of the equation `x^(2) -7x + 8 = 0` and the angle between these sides is `60^(@)` then the product of inradius an
Correct Answer - B Let a and b the roots of `x^(2) -7 x + 8 = 0` Then `a + b = 7, ab = 8` Also, `C = 60^(@)`...
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If vectors A, B, and C are three vectors, then which of the following is not correct?
Correct answer is (C) \(\vec{A}\times\vec{B} = \vec{B} \times \vec{A}\)
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The diagonal of the parallelogram made by two vectors as adjacent sides is not passing through common point of two vectors. What does it represent?
The diagonal of the parallelogram made by two vectors as adjacent sides not passing through common point of two vectors represents triangle law of vector addition.
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Given a = i + 2j and b = 2i + j, what are the magnitudes of the two vectors? Are these two vectors equal?
\(|\overset\rightarrow{a}|=\sqrt{1^2+2^2}=\sqrt{5}\) and \(|\overset\rightarrow{b}|=\sqrt{2^2+1^2}=\sqrt{5}\) The magnitudes of \(\overset\rightarrow{a}\) and \(\overset\rightarrow{b}\) are equal. However, their corresponding components are not equal, i.e., ax ≠ bx and ay ≠ by. Hence, the two vectors are not equal. Magnitudes of two vectors are equal, but vectors are unequal.
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The adjacent sides of a parallelogram are 36 cm and 27 cm in length .If the distance between the shorter sides is 12 cm , find the distance between th
Correct Answer - 9cm
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The midpoints of the sides BC, CA and AB of a `triangle ABC` are D(2,1), E(-5,7)and F-5, -5) respectively. Find the equations of the sides of `triangl
Correct Answer - x-2=0, 6x-7y+79=0, 6x+7y+65=0
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If two vertices of a parallelogram are `(3, 2), (-1, 0)` and the diagonals cut at `(2, -5)` , find the other vertices of the parallelogram.
Correct Answer - (1, -12);(5, -10)
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The difference between the lengths of the parallel sides of a trapezium is 8 cm, the perpendicular distance between these sides is 24 cm and the area
Correct Answer - 17 cm, 9 cm
2 Answers 1 views