Archive
3rd of March 2017
Mathematics
Q:

Find a unit vector in the XY plane which makes an angle of 45 degee with the vector i +j and an angle of 60 degree with the vector 3i-4j


The following question posed on 1st March on 3D has not been correctly replied : Find the vector and cartesian equation of the plane which bisects the line joining the points ....


The plane will pass through the midpoint of PQ and not through Q as mentioned in your answer


There have been errors in answers received to some more of the questions posed earlier which I will state later

Ahuja8087 Ahuja - CBSE - Class XII Science

Friday, March 03, 2017 at 17:44:PM

A:

begin mathsize 16px style Let space vector space be space ai plus bj.
Now comma
straight a with rightwards harpoon with barb upwards on top. straight b with rightwards harpoon with barb upwards on top equals open vertical bar straight a with rightwards arrow on top close vertical bar open vertical bar straight b with rightwards harpoon with barb upwards on top close vertical bar cosθ
straight a.1 plus straight b.1 equals 1 left parenthesis square root of 2 right parenthesis cos 45
straight a plus straight b equals 1
And comma space straight a squared plus straight b squared equals 1
rightwards double arrow left parenthesis straight a plus straight b right parenthesis squared minus straight a squared straight b squared equals 0
rightwards double arrow 2 ab equals 0
So comma space straight a equals 0 space or space straight b equals 0
straight a equals 1 space or space straight b equals 0
straight a equals 0 space or space straight b equals 1
straight a.3 minus plus straight b.4 equals 5 cos 60
rightwards double arrow 3 straight a minus 4 straight b equals 5 over 2
Thus comma space neither space straight a equals 1 space nor space straight b equals 1 space suit.
So comma space there space is space no space vector space in space xy space plane space which space satisfies space given space conditions. end style

Solution for 1st March Question

Error converting from MathML to accessible text.

Sorry for the inconvenience caused.

Friday, March 03, 2017 at 18:29:PM