10 Questions MCQ Test Mathematics (Maths) Class 12 - Test: Properties Of Vectors
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Any vector in an arbitrary direction can be replaced by two or three vectors
Detailed Solution for Test: Properties Of Vectors - Question 1
If we slide a vector parallel to its position it will be the same as before. Any vector in an arbitrary direction can always be replaced by two (or three) arbitrary vectors which have the original vector as their resultant.
The position vector of mid-point of joining the points (2, – 1, 3) and (4, 3, –5) is :
Detailed Solution for Test: Properties Of Vectors - Question 2
The position vector of point P = 2i - j + 3k
Position Vector of point Q = 4i + 3j - 5k
The position vector of R which divides PQ in half is given by:
r = (2i - j + 3k + 4i + 3j - 5k)/2
r = (6i + 2j - 2k)/2
r = 3i + j - k
The points with position vectors are collinear vectors, Value of a =
Detailed Solution for Test: Properties Of Vectors - Question 8
Position vector A = 60i+3j
Position vector B = 40i-8j
Position vector C = aj-52j
Now, find vector AB and BC
AB = -20i-11j
To be collinear, angle between the vector AB and BC made by the given position vectors should be 0 or 180 degree.
That’s why the cross product of the vectors should be zero
Therefore, a should be -40 to be the given positions vectors collinear.
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