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1st Year Mathematics Chapter 14 Test1st Year · Mathematics · Punjab (PTB)
Q1. Multiple choice questions (Attempt all · 10 × 1 = 10)
Angle in semi circle is:
A vector with magnitude 1 is called:
The angle between the vectors
is:
Moment of force F about a point with position vector r will be eqal to:
Vector product of two vector is a ......:
The dot product of vectors u and v is ......:
The magnitude of the vector v=ai+b
+ ck is:
Which of the following is a vector?
Projection of a vector v along u is:
The magnitude of dot an cross products of two vectors are 6 and
respectively then angle between vectors is ......:
Q2. Short questions (Attempt any 6 of 8 · 6 × 2 = 12)
Let u=3i+2j-5k, v=i-5j-k and w=-4i-j+7k. Find the following: I3v+wI.
Find the moment about the point M(-2,4,6) of the force represented by
, where coordinates of points A and B are (1,2,-3) and (3,-4,2) respectively.
Find the vector whose magnitude is 5 and is parallel to 3i+4j-k
Find a real number a so that the vectors u and v are perpendicular: u=ai+2aj-k, v=i+aj+3k
If u= xi + 2j + 3k, v=i+yj-3k and w=2i-3j represent the sides of a triangle. Find the values of x and y.
Find the magnitude of the vector v and write the direction cosines of v. v= - 6i+8j
If IaI=3, IbI=4 and Ia+bI=5. Find the angle between a and b.
Find a scalar a so the the vectors 2i+aj+5k and 3i+j+ak are orthogonal.
Q3. Long questions (Attempt any 2 of 3 · 2 × 4 = 8)
An electric shop sells three types of appliances. Fans, Heaters and Ovens. The monthly sales quantities are 500 units of Fans, 300 unit of Heaters and 200 units of Ovens. The profit per unit for each appliance is Rs 500 for Fans, Rs. 400 for Heater and Rs 2,000 for ovens.Calculate the total monthly profit using vector operations.
We say that two vectors v and w in space are parallel if there is a scalar c such that v=cw. The vectors point in the same direction of c>0 and the vectors point in the opposite direction if c<0. Find a vector of length 5 in the direction opposite that of v=i-2j+3k.
Show that for any vector a and b