A vector can be represented as a directed line segment in which length indicates ……………….. and arrow indicates ……………..
A) magnitude, direction
B) direction, magnitude
C) magnitude, speed
D) speed, velocity
1 Answers
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A line passes through the point (3,4,5) and is parallel to the vector `(2hat(i) +2hat(j) -3hat(k))` . Find the equations of the line in the vector as
Correct Answer - `vec(r )=(2hat(i)+4hat(j)+5hat(k)) +lambda(2hat(i) +2hat(j)-3hat(k)) ,(x-3)/(2)=(y-4)/(2)=(z-5)/(-3)`
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A line passes through the point (2,1,-3) and is parallel to the vector `(hat(i) -2hat(j) +2hat(k))` . Find the equations of the line in vector and Car
Correct Answer - `vec(r )=(2hat(i)-hat(j)-3hat(k)) +lambda (hat(i) -2hat(j)+3hat(k)) ,(x-2)/(1)=(y-1)/(-2)=(z+3)/(3)`
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Find the vector equations of the line passing through the point with position vector `(2hat(i) +hat(j) -5hat(k))` and parallel to the vector `(hat(i)
Correct Answer - `vec(r ) =(2hat(i) +hat(j) -5hat(k)) +lambda(hat(i) +3hat(j)-hat(k)) ,(x-2)/(1)=(y-1)/(3)=(z+5)/(-1)`
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Find the equations of the line passing through the point (1,-2,3) and parallel to the line `(x-6)/(3) =(y-2)/(-4) =(z+7)/(5)` Also find the vector for
Correct Answer - `(x-1)/(3)=(y+2)/(-4) =(z-3)/(5) , vec( r) =(hat(i) -2hat(j) +3hat(k)) +lambda (3hat(i) -4hat(j) +5hat(k))`
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The length of the perpendicular segment from the origin to a line is 2 units and the inclination of this perpendicular is `alpha` such that sin `alpha
Correct Answer - `2sqrt2x+y=0`
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Find the ratio in which the line segment having the end points `A(-1, -3, 4)` and `B(4, 2, -1) ` is divided by the `xz-`plane. Also, find the coordina
Correct Answer - `3:2` (2,0,1)
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(a) The length of Rameshs notebook is 9 cm 5 mm. What will be its length in cm? (b) The length of a young gram plant is 65 mm. Express its length in c
Correct Answer - (a) 9.5 सेमी: `" "`(b) 6.5 सेमी:
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12 In a plane electromagnetic wave, the directions of electric field and magnetic field are represented by \( \hat{ k } \) and \( 2 \hat{ i }-2 \hat{ j } \), respectively. What is the unit vector along direction of propagation of the wave? (a) \( \frac{1}{\sqrt{2}}(\hat{ i }+\hat{ j }) \) (b) \( \frac{1}{\sqrt{2}}(\hat{ j }+\hat{ k }) \) (c) \( \frac{1}{\sqrt{5}}(\hat{ i }+2 \hat{ j }) \) (d) \( \frac{1}{\sqrt{5}}(2 \hat{ i }+\hat{ j }) \)
Correct answer is (a) We know that propagation wave vector ∵ \(\vec{E} = \hat{k}\) \(\vec{B} = 2\hat{i} - 2\hat{j}\) \(\vec{C} = \vec{E} \times \vec{B}\) \(\vec{C} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 0 & 0 & 1...
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A line segment of length 7.8 cm is bisected then the length of each part is ……………..
Correct option is D) 3.9
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Find the vector joining the points P(2, 3, 0) and Q(– 1, – 2, – 4) directed from P to Q.
Given P(2,3,0) and Q (-1,-2,-4) P (2,3,0) Q (-1,-2,-4) PQ =(−1−2)i+(−2−3)j+(−4−0)k =−3i−5j−4k ∴ Vector jonining P and Q given by PQ =−3i−5j−4k.
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