What is the condition for the vectors 2i 3j 4k and 3i AJ BK to be parallel?

They can not be parallel. For them to be parallel the coefficients of i^,j^i^,j^ and k^k^ must be proportional.

For what value of a the vectors 2i 3j 4k and Ai 6j 8k − − are collinear?

In other words, the corresponding components of collinear vectors are proportional. Given vectors are 2i-3j+4k and ai+6j-8k. Therefore, the value of a is -4.

What is the condition for two vectors to be parallel to each other?

Two vectors A and B are parallel if and only if they are scalar multiples of one another. Complete step-by-step answer: Two vectors A and B are parallel if and only if they are scalar multiples of one another. , k is a constant not equal to zero.

How do you find the area of a parallelogram with 3 vertices?

Find the area of the parallelogram by calculating the magnitude of the cross product using the formula √(x^2 + y^2 + z^2).

How do you find the projection of a vector?

Summary

1. The vector projection of a vector onto a given direction has a magnitude equal to the scalar projection.
2. The formula for the projection vector is given by projuv=(u⋅v|u|)u|u|.
3. A vector →v is multiplied by a scalar s.
4. A scalar projection is the length of the vector projection.

How do you find the area of a parallelogram formed by vectors?

In this section, you will learn how to find the area of parallelogram formed by vectors. Find the area of the parallelogram whose two adjacent sides are determined by the vectors i vector + 2j vector + 3k vector and 3i vector − 2j vector + k vector. b vector = 3i vector − 2j vector + k vector.

What is the value of cos(θ) for a parallel vector?

If parallel, then cos (θ) = 1 for θ=0, -1 for θ=π … this is another way of saying that ‘a’ and ‘b’ are scalar multiples of each other, when parallel… a = kb If I look at the ‘i’ components of both vectors, multiply a = i-2j+3k by -1 to match b vectors ‘-i’ component, I get -i +2j-3k which is not -i+j+2k, so not parallel.

How do you find the angle between two vectors?

For determining the angle between two vectors, we use the dot product which is as follows: For A.B we will simply multiply the values of similar directions and then add them. You may be familiar with the dot or scalar product of vectors. For determining the angle between two vectors, we use the dot product which is as follows:

How to find the area of a triangle with three vectors?

Expression to find the area of a triangle when three vectors will be given. Let the sides of ∆ABC be represented by a ⃗, b ⃗ a n d c ⃗ \\vec a, \\vec b\\ and\\ \\vec c a, b a n d c. Basically they will give us the position vectors of the corresponding sides. If they are the position vectors of the ∆ABC then the area of the triangle will be written as