- Position Vector
- Direction Cosines and Direction Ratios of a Vector
- Position Vector
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- Vector Algebra part 4 (Direction Angle, Direction cosine)
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- Direction cosine and Direction ratio
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- Vector Algebra part 3 (Position Vector)
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Find the position vector of a point which divides the join of points with position vectors `veca-2vecb" and "2veca+vecb`externally in the ratio 2 : 1
If θ is the angle between two vectors `veca` and `vecb`, then `veca.vecb >= 0` only when
(A) `0 < theta < pi/2`
(B) `0 <= theta <= pi/2`
(C) `0 < theta < pi`
(D) `0 <= theta <= pi`
Classify the following measures as scalars and vectors.
(i) 10 kg
(ii) 2 metres north-west
(iv) 40 watt
(v) 10–19 coulomb
(vi) 20 m/s2
Find the position vector of the foot of perpendicular and the perpendicular distance from the point P with position vector
`2hati+3hatj+4hatk` to the plane `vecr` . `(2hati+hatj+3hatk)−26=0` . Also find image of P in the plane.
Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are `hati + 2hatj - hatk` and `-hati + hatj + hatk` respectively, in the ration 2:1
Let `veca` and `vecb` be two unit vectors andθ is the angle between them. Then `veca + vecb` is a unit vector if
(A) `theta = pi/4`
(B) `theta = pi/3`
(C) `theta =pi/2`
(D) `theta = 2pi/3`
Find the direction cosines of the vector joining the points A (1, 2, –3) and B (–1, –2, 1) directed from A to B.
Show that the points A, B and C with position vectors `veca = 3hati - 4hatj - 4hatk`, `vecb = 2hati - hatj + hatk` and `vecc = hati - 3hatj - 5hatk` respectively form the vertices of a right angled triangle.
Classify the following as scalar and vector quantities.
(i) time period
(v) work done
Write the position vector of the point which divides the join of points with position vectors `3veca-2vecb and 2veca+3vecb` in the ratio 2 : 1.