Question
Let a line pass through the origin and make equal angles
with the coordinate axes. Then the direction cosines of the line are:Solution
Let the direction cosines be l, m, n.
If the line makes equal angles with the coordinate axes, then: l = m = n And we know the identity for direction cosines:
l² + m² + n² = 1 Substitute l = m = n: ⇒ 3l² = 1
⇒ l² = 1/3
⇒ l = m = n = 1/√3 So, the direction cosines are (1/√3, 1/√3, 1/√3)
Quantity I: A shopkeeper sold an article for Rs.1500 and made a profit of Y%. If he increases the selling price by Rs.400, he can make a profit of (Y +...
The average weight of 12 children rises by 2.15 kg after one of the children, who weighs 56 kg, is replaced by a new child. What is the weight of the ne...
A train that is 300 meters long takes 15 seconds to pass a tree. What is the speed of the train in kilometers per hour?
The average scores of candidates from Institute A and Institute B in a Mock test (out of 150 marks) are 80 and 90, respectively. The number of candidate...
A spherical metallic shell with 6 cm external radius weighs 6688 g. What is the thickness of the shell if the density of metal is 10.5 g per cm3
Find the equation if a point P(x, y) is equidistant from A(7, 3) and B(-3, 7).
Which of the following options best defines the term 'Bandwidth'?
A builder needs to transport sand and gravel. A truck can carry 4 tons of sand and 3 tons of gravel. A van can carry 2 tons of sand and 2 tons of grave...
If sin x + sin y = a and cos x + cos y = b, find sin(x + y):
Relevant for Exams:
