Class 12

Math

Algebra

Vector Algebra

The scalar product of the vector $i^+j^ +k^$with a unit vector along the sum of vector $2i^+4j^ −5k^$and $λi^+2j^ +3k^$is equal to one. Find the value of $λ$.

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

If $a,bandc$ are three non-zero vectors, no two of which ar collinear, $a+2b$ is collinear with $c$ and $b+3c$ is collinear with $a,$ then find the value of $∣∣ a+2b+6c∣∣ ˙$

A man travelling towards east at 8km/h finds that the wind seems to blow directly from the north On doubling the speed, he finds that it appears to come from the north-east. Find the velocity of the wind.

If $A(−4,0,3)andB(14,2,−5),$ then which one of the following points lie on the bisector of the angle between $OAandOB(O$ is the origin of reference )? a. $(2,2,4)$ b. $(2,11,5)$ c. $(−3,−3,−6)$ d. $(1,1,2)$

Let $A(t)=f_{1}(t)i^+f_{2}(t)j^ andB(t)=g(t)i^+g_{2}(t)j^ ,t∈[0,1],f_{1},f_{2},g_{1}g_{2}$ are continuous functions. If $A(t)andB(t)$ are non-zero vectors for all $tandA(0)=2i^+3j^ ,A(1)=6i^+2j^ ,B(0)=3i^+2i^andB(1)=2j^ +6j^ $ Then,show that $A(t)andB(t)$ are parallel for some $t$.

A unit vector of modulus 2 is equally inclined to $x$ - and $y$ -axes at an angle $π/3$ . Find the length of projection of the vector on the $z$ -axis.

Let $a,b,andc$ be any three vectors, then prove that $[a×bb×cc×a]=[abc]_{2}˙$

Check whether the three vectors $2i^+2j^ +3k^,−3i^+3j^ +2k^and3i^+4k^$ from a triangle or not

A vector has components $p$ and 1 with respect to a rectangular Cartesian system. The axes are rotted through an angel $α$about the origin the anticlockwise sense. Statement 1: IF the vector has component $p+2$and 1 with respect to the new system, then $p=−1.$ Statement 2: Magnitude of the original vector and new vector remains the same.