Solution: CORRECT OPTION: (B) as the ques suggests,
The angle between two vectors a and b with magnitudes √3 and 4, respectively, and a.b=2×3^1/2 is
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Vector Algebra
The vector having initial and terminal points as (2, 5, 0) and (–3, 7, 4), respectively is (A)-i+12j+4k (B)5i+2j-4k (C)-5i+2j+4k (D)i+j+k
CORRECT OPTION: \[\left( C \right)-5i+2j+4k\] Let us take, A and B be the pints with coordinates (2, 5, 0) and (-3, 7, 4) respectively. Hence,
The position vector of the point which divides the join of points 2a-3b and a+b in the ratio 3 : 1 is (A) (3a-2b)/2 (B) (7a-8b)/4 (C) 3a/4 (D) 5a/4
CORRECT ANSWER: \[\left( D \right)5a/4~\] ACCORDING TO QUES , Given ratio is 3:1
The vector in the direction of the vector i-2j+k that has magnitude 9 is (A) i-2j+2k (B)(i-2j+2k)/3 (C)3(i-2j+2k) (D)9(i-2j+2k)
CORRECT ANSWER: \[\left( C \right)\text{ }3\left( i-2j+2k \right)\]
If a=i+j+k and b=j-k, find a vector c such that axc=b and a.c=3
according to ques,
Show that area of the parallelogram whose diagonals are given by a and b is (axb)/2. Also find the area of the parallelogram whose diagonals are 2i-j+k and i+3j-k
according to ques,
If a,b,c determine the vertices of a triangle, show that ½[bxc+cxa+axb] gives the vector area of the triangle. Hence deduce the condition that the three points a,b,c are collinear. Also find the unit vector normal to the plane of the triangle.
according to ques,
Prove that in any triangle ABC, , where a, b, c are the magnitudes of the sides opposite to the vertices A, B, C, respectively.
according to ques,
Using vectors, prove that the parallelogram on the same base and between the same parallels are equal in area.
According to ques, proved.
Using vectors, find the area of the triangle ABC with vertices A(1, 2, 3), B(2, – 1, 4) and C(4, 5, – 1).
according to ques,
If A, B, C, D are the points with position vectors i+j-k, 2i-j+3k, 2i-3k, 3i-2j+k respectively, find the projection of AB along CD.
According to ques,
Find the sine of the angle between the vectors a=3i+j+2k and b=2i-2j+4k
according to ques,
If a+b+c=0 , show that axb=bxc=cxa . Interpret the result geometrically?
according to ques,
Find the angle between the vectors:2i-j+k and 3i+4j-k.
according to ques,
Find a vector of magnitude 6, which is perpendicular to both the vectors 2i-j+2k and 4i-j+3k .
according to ques,
A vector r has magnitude 14 and direction ratios 2, 3, – 6. Find the direction cosines and components of r , given that r makes an acute angle with x-axis.
According to ques,
A vector r is inclined at equal angles to the three axes. If the magnitude of r is 2√3 units, find r.
Since, vector makes equal angles with the axes, their direction cosines will be same hence, \[~l\text{ }=\text{ }m\text{ }=\text{ }n\] also, \[{{l}^{2}}~+\text{ }{{m}^{2}}~+\text{...
Using vectors, find the value of k such that the points (k, – 10, 3), (1, –1, 3) and (3, 5, 3) are collinear.
according to ques,
If a and b are the position vectors of A and B, respectively, find the position vector of a point C in BA produced such that BC = 1.5 BA.
According to ques,
Find a unit vector in the direction of PQ where P and Q have co-ordinates (5, 0, 8) and (3, 3, 2), respectively.
According to ques,
If a=i+j+2k and b=2i+j-2k find the unit vector in the direction of (i)6b (ii)2a-b
According to ques,
Find the unit vector in the direction of sum of vectors:
according to ques,