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If vectors î-3 ĵ+5 k̂ and î-3 ĵ-a k̂ are equal vectors then the value of a is: a. 5 b. 4 c. -4 d....
The angle which the vector A⃗=2 î+3 ĵ makes with the y-axis, where î and ĵ are unit vectors along...
If the vectors 2 𝐢̂-3 𝐣̂, 𝐢̂+𝐣̂-𝐤̂ and 3 𝐢̂-𝐤̂ form three concurrent edges of a parallelop...
Let a⃗=2 î+3 ĵ-6 k̂, b⃗=2 î-3 ĵ+6 k̂ and c⃗=-2 î+3 ĵ+6 k̂. Let a_1 be the projection of a⃗ on b⃗ ...
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The vector that must be added to the vector î-3 ĵ+2 k̂ and 3 î+6 ĵ-7 k̂ so that the resultant vec...
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Given three vectors 𝐚=6 𝐢̂-3 𝐣̂, 𝐛=2 𝐢̂-6 𝐣̂ and c=-2 𝐢̂+21 𝐣̂ such that α=𝐚+𝐛+𝐜. Then...
If the vector 6 î-3 ĵ-6 k̂ is decomposed into vectors parallel and perpendicular to the vectorî+ĵ...
The components of the sum of two vectors 2 î+3 ĵ and 2 ĵ+3 k̂ along x and y directions respective...
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Show that the vectors : 2 î-ĵ+k̂, î-3 ĵ-5 k̂ and 3 î-4 ĵ-4 k̂ form the vertices of a right angled...
Given : A⃗=2 î-3 ĵ-k̂ and B⃗=-6 î+9 ĵ+3 k̂ which of the following statements is correct? (a) A⃗ a...
Consider a uniform electric field E = 3 × 103 î N/C. (a) What is the flux of this field through a sq
Consider a vector F⃗=4 î-3 ĵ. Another vector that is perpendicular to F⃗ is (a) 4 î+3 ĵ (b) 6 î (...
Two vectors are given by A⃗=(3 î+ĵ+3 k̂) and B⃗=(3 î+5 ĵ-2 k̂). Find the third vector C⃗ if A⃗+3 ...
, , The position vector of a particle is (2 î-3 ĵ+k̂) m. Calculate the ĵ^th component of torque o...
Show that the vectors 2 𝐢̂-𝐣̂+𝐤̂ and 𝐢̂-3 𝐣̂-5 𝐤̂ are at right angles.
𝐀, 𝐄 and 𝐂 are three vectors given by 2 𝐢̂+𝐤̂, 𝐢̂+𝐣̂+𝐤̂ and 4 î-3 ĵ+7 k̂ Then, find R, wh...
Two forces F⃗_1=2 î+2 ĵN and F_2=3 ĵ+4 k̂ N are acting on a particle. The resultant force acting...
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If A=3 î+5 ĵ-7 k̂, the direction of cosines of the vector A are: a. 2/√(83), 5/√(83), 7/√(83) b. ...
Given three vectors a⃗=6 î-3 ĵ, b⃗=2 î-6 ĵ and c⃗=-2 î+21 ĵ such that α⃗=a⃗+b⃗+c⃗. Then the resol...
Let √(3)𝐢̂+𝐣̂, 𝐢̂+√(3)𝐣̂ and β𝐢̂+(1-β) 𝐣̂ respectively be the position vectors of the point...
The angle that the vector A=2 î+3 ĵ makes with y-axis is- (1) tan ^-1(3 / 2) (2) tan ^-1(2 / 3) (...
Unit vector of 4 𝐢̂-3 𝐣̂+𝐤̂ is (a) 𝐢̂-𝐣̂+𝐤̂ (b) √(26)𝐢̂-√(26)𝐣̂+√(26)𝐤̂ (c) 4 𝐢̂-3 𝐣̂+...
Find the angle between the vectors î-2 ĵ+3 k̂ and 3 î-2 ĵ+k̂.
A particle moves from position 3 î+5 ĵ-8 k̂ to 15 î-20 ĵ+8 k̂ due to uniform force of (3 î+ĵ+4 k̂...
If the vector 6 î-3 ĵ-6 k̂ is decomposed into vectors parallel and perpendicular to the vector î+...
A ray of light moving along vector (3 √(2)î-3 ĵ-3 k̂) under goes refraction at an interface of tw...
If 𝐚=𝐢̂+2 𝐣̂+3 𝐤̂, 𝐛=-𝐢̂+2 𝐣̂+𝐤̂ and 𝐜=3 𝐢̂+𝐣̂, then the unit vector along its resulta...
, , Shows that the vector A̅=2 î-3 ĵ-k̂ and B⃗=-6 î+9 ĵ+3 k̂ are parallel.W,
If 𝐚=𝐢̂+𝐣̂+𝐤̂, 𝐛=4 𝐢̂+3 𝐣̂+4 𝐤̂ and 𝐜=𝐢̂+α𝐣̂+β𝐤̂ are linearly dependent vectors and |...
Let √(3)î+ĵ, î+√(3)ĵ and βî+(1-β) ĵ respectively be the position vectors of the points A, B and C...
A vector (d) is equally inclined to three vectors 𝐚=𝐢̂-𝐣̂+𝐤̂, 𝐛=2 𝐢̂+𝐣̂ and 𝐜=3 𝐣̂-2 𝐤̂...
If vector a=2 𝐢̂-3 𝐣̂+6 𝐤̂ and vector 𝐛=-2 𝐢̂+2 𝐣̂-𝐤̂, then Projection of vector a on vect...
The force 7 î+3 ĵ-5 k̂ acts on a particle whose position vector is î-ĵ+k̂. What is the torque of ...
What should be added in vector a=3 î+4 𝐣̂-2 𝐤̂ to get its resultant a unit vector 𝐢̂ ? (a) -2 ...
Find the angle between the vectors 2 î-ĵ+k̂ and 3 î+4 ĵ-k̂. a⃗ and b⃗ angle b / ω a⃗ and b⃗ ...
, , lor the given vector A=3 î-4 ĵ+10 k̂, theratio of magnitude of its component on the x-y plane...
Let PR=3 î+ĵ-2 k̂ and SQ=î-3 ĵ-4 k̂ determine diagonals of a parallelogram PQRS and PT=î+2 ĵ+3 k̂...
If a⃗=3 î-ĵ+2 k̂ and b⃗=-î-2 ĵ+4 k̂, find a unit vector along the vector (a⃗×b⃗).
The vectors 3 î-2 ĵ+k̂, î-3 ĵ+5 k̂& 2 î+ĵ-4 k̂ form the sides of a triangle. Then triangle is (A)...
A particle has initial velocity (2 î+3 ĵ) and acceleration (0.3 i⃗+0.2 j⃗). The magnitude of velo...
Show that the vectors 2 î-3 ĵ+4 k̂ and -4 î+6 ĵ-8 k̂ are collinear. Two vectors p⃗+q⃗ are collina...
If A=3 î+4 ĵ and B=7 î+24 ĵ the vector having the same magmitude as B and parallel to A is (a) 5 ...
The points with position vectors 60 𝐢̂+3 𝐣̂, 40 𝐢̂-8 𝐣̂, a 𝐢̂-52 𝐣̂ are collinear, if (1983...
Find λ and μ if (î+3 ĵ+9 k̂) ×(3 î-λĵ+μk̂)=0