Applications of Dot Product
Trending Questions
Q. Let u, v, w be such that |u|=1, |v|=2, |w|=3. If the projection v along u is equal to that of w along u and v, w are perpendicular to each other then |u-v+w| =
- 2
- √14
- √7
- 14
Q. If a+b+c=0 and |a|=3, |b|=4 and |c|=√37, the angle between a and b is
- π3
- π4
- π2
- π6
Q. If f2(x)+2g2(x)+3h2(x)≤1 and u(x)=2f(x)−2g(x)+3h(x), then the maximum value of u2(x) is equal to
Q. If, in a right angled triangle ABC, the hypotenuse AB = p, then AB . AC + BC . BA + CA . CB =
- 2p2
- p22
- p2
- None
Q. The length of the projection of 2^i−3^j+^k in the direction of 4^i−4^j+7^k is
- 3
- 9
- 27
- 3√3
Q. If a=4^i+6^j and b=3^j+4^k, then the vector form of the component of a along b is
- 18(3^j+4^k)10√3
- 18(3^j+4^k)25
- 18(3^j+4^k)√13
- 3^j+^k
Q. If |a|=3, |b|=4 and |a+b|=1, then |a-b|=
- 5
- 6
- 7
- 8
Q. If a=−^i+2^j+3^k and b=^i−2^j+^k, c=4^i−3^j−2^k and a+λb is perpendicular to c, then λ =
- 1
- 3
- 2
- 4
Q. Let a and b be two unit vectors. If the vectors c=a+2b and d=5a-4b are perpendicular to each other, then the angle between a and b is
- π3
- π4
- π6
- π2
Q. A particle acted on by constant forces 4^i+^j−3^k and 3^i+^j−^k is displaced from the point ^i+2^j+3^k to the point 5^i+4^j+^k. The total work done by the forces is
- 20 units
- 30 units
- 40 units
- 50 units